%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWW211+1 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n024.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 13:22:08 EDT 2022 % Result : Unknown 11.02s 10.98s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SWW211+1 : TPTP v8.1.0. Released v5.2.0. % 0.02/0.12 % Command : otter-tptp-script %s % 0.12/0.33 % Computer : n024.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jul 27 02:53:40 EDT 2022 % 0.12/0.33 % CPUTime : % 10.94/10.89 ----- Otter 3.3f, August 2004 ----- % 10.94/10.89 The process was started by sandbox2 on n024.cluster.edu, % 10.94/10.89 Wed Jul 27 02:53:40 2022 % 10.94/10.89 The command was "./otter". The process ID is 31033. % 10.94/10.89 % 10.94/10.89 set(prolog_style_variables). % 10.94/10.89 set(auto). % 10.94/10.89 dependent: set(auto1). % 10.94/10.89 dependent: set(process_input). % 10.94/10.89 dependent: clear(print_kept). % 10.94/10.89 dependent: clear(print_new_demod). % 10.94/10.89 dependent: clear(print_back_demod). % 10.94/10.89 dependent: clear(print_back_sub). % 10.94/10.89 dependent: set(control_memory). % 10.94/10.89 dependent: assign(max_mem, 12000). % 10.94/10.89 dependent: assign(pick_given_ratio, 4). % 10.94/10.89 dependent: assign(stats_level, 1). % 10.94/10.89 dependent: assign(max_seconds, 10800). % 10.94/10.89 clear(print_given). % 10.94/10.89 % 10.94/10.89 formula_list(usable). % 10.94/10.89 all A (A=A). % 10.94/10.89 all V_gb_2 V_fa_2 ((all B_x (hAPP(V_fa_2,B_x)=hAPP(V_gb_2,B_x)))->V_fa_2=V_gb_2). % 10.94/10.89 c_SEQ_Osubse_q(v_f____). % 10.94/10.89 c_SEQ_Osubse_q(v_ga____). % 10.94/10.89 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e____). % 10.94/10.89 c_SEQ_Osubse_q(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)). % 10.94/10.89 all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_s(B_n)),v_r). % 10.94/10.89 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 10.94/10.89 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)))). % 10.94/10.89 c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N1____,hAPP(v_ga____,v_n____)). % 10.94/10.89 all V_real2_H_2 V_real1_H_2 V_real2_2 V_real1_2 (c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)<->V_real1_2=V_real1_H_2&V_real2_2=V_real2_H_2). % 10.94/10.89 all V_h_2 V_gb_2 T_d V_fa_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2)). % 10.94/10.89 all V_xa_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_xa_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))). % 10.94/10.89 all T_e T_d T_c T_a T_b V_x_H_2 V_g_H_2 V_f_H_2 V_xa_2 V_gb_2 V_fa_2 (hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))->hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_xa_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2)). % 10.94/10.89 all V_v_2 V_c_2 V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=V_c_2->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2)). % 10.94/10.89 all V_v_2 V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2))). % 10.94/10.89 all V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)-> (all B_v (hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v))))). % 10.94/10.89 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r). % 10.94/10.89 c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N2____,v_n____). % 10.94/10.89 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))). % 10.94/10.89 all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.89 all V_xa_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_xa_2<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.89 all V_xa_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_RealVector_Onorm__class_Onorm(T_a,V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_xa_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)). % 10.94/10.89 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2)))). % 10.94/10.89 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)). % 10.94/10.89 all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a). % 10.94/10.89 all V_xa_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_xa_2))<->V_xa_2!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.89 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 10.94/10.89 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.89 all V_d V_c V_b V_a (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d))). % 10.94/10.89 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (V_a_2=V_b_2<->V_c_2=V_d_2))). % 10.94/10.89 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_s(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),v_r). % 10.94/10.89 c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),v_n____). % 10.94/10.89 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)). % 10.94/10.89 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)). % 10.94/10.89 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)). % 10.94/10.89 all V_na_2 V_fa_2 (c_SEQ_Osubse_q(V_fa_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,hAPP(V_fa_2,V_na_2))). % 10.94/10.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2). % 10.94/10.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)&V_xa_2!=V_ya_2). % 10.94/10.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.89 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 10.94/10.89 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 10.94/10.89 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))). % 10.94/10.89 all V_c_2 V_b_2 V_a_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)<->V_b_2=V_c_2)). % 10.94/10.89 all V_c_2 V_a_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)<->V_b_2=V_c_2)). % 10.94/10.89 all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))). % 10.94/10.89 all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)). % 10.94/10.89 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)). % 10.94/10.89 all V_y V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))). % 10.94/10.89 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s))))). % 10.94/10.89 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a). % 10.94/10.89 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a). % 10.94/10.89 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a). % 10.94/10.89 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 10.94/10.89 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 10.94/10.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))). % 10.94/10.89 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))). % 10.94/10.89 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))). % 10.94/10.89 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))). % 10.94/10.89 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))). % 10.94/10.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))). % 10.94/10.89 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 10.94/10.89 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a). % 10.94/10.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a). % 10.94/10.89 all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))). % 10.94/10.89 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))). % 10.94/10.89 all V_d V_c V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.89 all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))). % 10.94/10.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))). % 10.94/10.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))). % 10.94/10.89 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))). % 10.94/10.89 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.89 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))). % 10.94/10.89 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))). % 10.94/10.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))). % 10.94/10.89 all V_xa_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2)))). % 10.94/10.89 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))). % 10.94/10.89 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))). % 10.94/10.89 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))). % 10.94/10.89 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))). % 10.94/10.89 all V_xa_2 V_ya_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))). % 10.94/10.89 all V_xa_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2)))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (V_xa_2=V_ya_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)). % 10.94/10.89 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x),hAPP(V_gb_2,B_x))))). % 10.94/10.89 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (V_xa_2!=V_ya_2<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2)). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)). % 10.94/10.89 all V_xa_2 V_ya_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)). % 10.94/10.89 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))). % 10.94/10.89 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))). % 10.94/10.89 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))). % 10.94/10.89 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))). % 10.94/10.89 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 10.94/10.89 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 10.94/10.89 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)->V_z=V_w)). % 10.94/10.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k))). % 10.94/10.89 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)). % 10.94/10.89 all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w). % 10.94/10.89 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)&V_xa_2!=V_ya_2)). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2)). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))). % 10.94/10.89 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))). % 10.94/10.89 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.89 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))). % 10.94/10.89 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))). % 10.94/10.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))). % 10.94/10.89 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)). % 10.94/10.89 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.89 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))). % 10.94/10.89 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))). % 10.94/10.89 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 10.94/10.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.89 all V_real2 V_real1 (c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))). % 10.94/10.89 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))). % 10.94/10.89 all V_na_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)). % 10.94/10.89 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))). % 10.94/10.89 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.89 all V_real2 V_real1 (c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))). % 10.94/10.89 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2))). % 10.94/10.89 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)). % 10.94/10.89 all V_d V_c V_b V_a (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d))). % 10.94/10.89 all V_z V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))). % 10.94/10.89 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))). % 10.94/10.89 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))). % 10.94/10.89 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))). % 10.94/10.89 all V_a V_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)). % 10.94/10.89 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)). % 10.94/10.89 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m). % 10.94/10.89 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_P_2 V_na_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)->hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)))-> ((V_m_2=V_na_2->hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2))))). % 10.94/10.89 all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))). % 10.94/10.89 all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)). % 10.94/10.89 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t). % 10.94/10.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n). % 10.94/10.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)). % 10.94/10.89 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))). % 10.94/10.89 all V_na_2 V_m_2 (V_m_2!=V_na_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)). % 10.94/10.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)). % 10.94/10.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)). % 10.94/10.89 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))). % 10.94/10.89 all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))). % 10.94/10.89 all V_na_2 V_m_2 V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2)<->V_m_2=V_na_2). % 10.94/10.89 all V_na_2 V_k_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_na_2,V_k_2)<->V_m_2=V_na_2). % 10.94/10.89 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))). % 10.94/10.89 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m). % 10.94/10.89 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m). % 10.94/10.89 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n). % 10.94/10.89 all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)). % 10.94/10.89 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))). % 10.94/10.89 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))). % 10.94/10.89 all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i). % 10.94/10.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)). % 10.94/10.89 all V_na_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2)<->V_m_2=V_na_2))). % 10.94/10.89 all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))). % 10.94/10.89 all V_na_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)))). % 10.94/10.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.89 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))). % 10.94/10.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.89 all V_m_2 V_na_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)). % 10.94/10.89 all V_na_2 (V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)). % 10.94/10.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_na_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m). % 10.94/10.89 all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n). % 10.94/10.89 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 10.94/10.89 all V_na_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_na_2 V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_na_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)). % 10.94/10.89 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 10.94/10.89 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))). % 10.94/10.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))). % 10.94/10.89 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))). % 10.94/10.89 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))). % 10.94/10.89 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m). % 10.94/10.89 all V_na_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)). % 10.94/10.89 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)). % 10.94/10.89 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)). % 10.94/10.89 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)). % 10.94/10.89 all V_na_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)&V_m_2!=V_na_2). % 10.94/10.89 all V_na_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2=V_na_2). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 10.94/10.89 all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))). % 10.94/10.89 all V_na_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)))). % 10.94/10.89 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)). % 10.94/10.89 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)). % 10.94/10.90 all V_na_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)<-> (exists B_k (V_na_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))). % 10.94/10.90 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)). % 10.94/10.90 all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))). % 10.94/10.90 all V_na_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)). % 10.94/10.90 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))). % 10.94/10.90 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))). % 10.94/10.90 all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))). % 10.94/10.90 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))). % 10.94/10.90 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m). % 10.94/10.90 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)). % 10.94/10.90 all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))). % 10.94/10.90 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m). % 10.94/10.90 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))). % 10.94/10.90 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))). % 10.94/10.90 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)). % 10.94/10.90 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)). % 10.94/10.90 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))). % 10.94/10.90 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),c_Complex_ORe(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),c_Complex_OIm(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))))). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))). % 10.94/10.90 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))). % 10.94/10.90 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a). % 10.94/10.90 all V_a_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))). % 10.94/10.90 all V_z (c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z))=V_z). % 10.94/10.90 all V_r (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)). % 10.94/10.90 all V_ya_2 V_xa_2 (V_xa_2=V_ya_2<->c_Complex_ORe(V_xa_2)=c_Complex_ORe(V_ya_2)&c_Complex_OIm(V_xa_2)=c_Complex_OIm(V_ya_2)). % 10.94/10.90 all V_y V_x (c_Complex_ORe(V_x)=c_Complex_ORe(V_y)-> (c_Complex_OIm(V_x)=c_Complex_OIm(V_y)->V_x=V_y)). % 10.94/10.90 all V_y V_x (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)))). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.90 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 10.94/10.90 all V_y V_x (c_Complex_OIm(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y))). % 10.94/10.90 all V_y V_x (c_Complex_ORe(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y))). % 10.94/10.90 all V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a)). % 10.94/10.90 all V_y V_x (c_Complex_OIm(c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y). % 10.94/10.90 all V_y V_x (c_Complex_ORe(c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x). % 10.94/10.90 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y))))). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)). % 10.94/10.90 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)). % 10.94/10.90 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.90 c_Complex_OIm(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 c_Complex_ORe(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 all V_y V_x (c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y))). % 10.94/10.90 all V_y V_x (c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))). % 10.94/10.90 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))). % 10.94/10.90 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)). % 10.94/10.90 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))). % 10.94/10.90 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)). % 10.94/10.90 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))). % 10.94/10.90 all B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)-> (exists B_n0 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_n0,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),B_r)))). % 10.94/10.90 all B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)-> (exists B_n0 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_n0,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),B_r)))). % 10.94/10.90 all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(v_s(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_ra_2 V_a_2 V_xa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_ra_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_xa_2)&c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)))). % 10.94/10.90 all V_X_2 V_K_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)-> ((all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2))->c_SEQ_OBse_q(T_a,V_X_2)))). % 10.94/10.90 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))). % 10.94/10.90 all V_xa_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_xa_2<->V_xa_2=c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.90 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.90 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.90 all V_x (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))). % 10.94/10.90 all V_X_2 V_M_2 T_a T_b (class_RealVector_Oreal__normed__vector(T_b)&class_Orderings_Oord(T_a)-> ((all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))-> (all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))))))). % 10.94/10.90 all V_b V_x V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_a,B_y)&c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_y,V_b))))))). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))))). % 10.94/10.90 all V_K_2 V_X_2 V_N_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> ((all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2,B_n)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)))->c_SEQ_OBse_q(T_a,V_X_2))). % 10.94/10.90 all V_b V_x V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b))))))). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N1____,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N2____,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber__ring(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_ya_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2))). % 10.94/10.90 all V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 all V_x (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=V_x). % 10.94/10.90 all V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 all V_w T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w))). % 10.94/10.90 all T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 all V_w T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))). % 10.94/10.90 all V_k (c_Int_OBit1(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k)). % 10.94/10.90 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)&class_RealVector_Oreal__normed__field(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))). % 10.94/10.90 all T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 all V_ya_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2))). % 10.94/10.90 all V_w T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))). % 10.94/10.90 all V_ya_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_ya_2))). % 10.94/10.90 all V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OPls))). % 10.94/10.90 all V_a V_b T_a (class_RealVector_Oreal__normed__field(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))). % 10.94/10.90 all V_ya_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2))). % 10.94/10.90 all V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls))). % 10.94/10.90 all V_w T_a (class_Int_Onumber__ring(T_a)&class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w))). % 10.94/10.90 c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.90 all T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OPls). % 10.94/10.90 all V_l (c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l))). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2)). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2)). % 10.94/10.90 all V_k (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls)=V_k). % 10.94/10.90 all V_x T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,c_Int_OPls)). % 10.94/10.90 all V_l V_k (c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_l V_k (c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l))=c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_l V_k (c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 c_Int_OBit0(c_Int_OPls)=c_Int_OPls. % 10.94/10.90 all V_l (c_Int_OPls!=c_Int_OBit1(V_l)). % 10.94/10.90 all V_l_2 (c_Int_OPls=c_Int_OBit0(V_l_2)<->c_Int_OPls=V_l_2). % 10.94/10.90 all V_a T_a (class_Fields_Ofield(T_a)&class_Int_Onumber__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_a). % 10.94/10.90 all V_x T_a (class_Fields_Ofield(T_a)&class_Int_Onumber__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_x). % 10.94/10.90 all V_k (c_Int_OBit1(V_k)!=c_Int_OPls). % 10.94/10.90 all V_k_2 (c_Int_OBit0(V_k_2)=c_Int_OPls<->V_k_2=c_Int_OPls). % 10.94/10.90 all V_xa_2 V_w_2 T_a (class_Int_Onumber(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=V_xa_2<->V_xa_2=c_Int_Onumber__class_Onumber__of(T_a,V_w_2))). % 10.94/10.90 all V_l V_k (c_Int_OBit0(V_k)!=c_Int_OBit1(V_l)). % 10.94/10.90 all V_l V_k (c_Int_OBit1(V_k)!=c_Int_OBit0(V_l)). % 10.94/10.90 all V_l_2 V_k_2 (c_Int_OBit0(V_k_2)=c_Int_OBit0(V_l_2)<->V_k_2=V_l_2). % 10.94/10.90 all V_l_2 V_k_2 (c_Int_OBit1(V_k_2)=c_Int_OBit1(V_l_2)<->V_k_2=V_l_2). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Int_Oring__char__0(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)<->V_xa_2=V_ya_2)). % 10.94/10.90 all V_k (c_Int_OBit0(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k)). % 10.94/10.90 all V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k)=V_k). % 10.94/10.90 all V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls)=V_k). % 10.94/10.90 all V_a T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))=V_a). % 10.94/10.90 all V_a T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a)=V_a). % 10.94/10.90 all V_l V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_l V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l))=c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_l V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l))=c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_r T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_a V_b (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all V_b V_a (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_k2_2 V_k1_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)). % 10.94/10.90 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)). % 10.94/10.90 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)). % 10.94/10.90 all V_ra_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2))). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2)). % 10.94/10.90 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2)). % 10.94/10.90 -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls). % 10.94/10.90 all V_y T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2))). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2))). % 10.94/10.90 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))). % 10.94/10.90 all V_z V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z)). % 10.94/10.90 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))). % 10.94/10.90 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))). % 10.94/10.90 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))). % 10.94/10.90 all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a). % 10.94/10.90 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))). % 10.94/10.90 all V_w_2 V_v_2 T_a (class_Int_Onumber(T_a)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))<-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)))). % 10.94/10.90 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (V_a=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a))& (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all V_a_2 V_b_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_b_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)=c_Groups_Oone__class_Oone(T_a)<->V_a_2=V_b_2))). % 10.94/10.90 all V_c V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c)). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))<-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2))& (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))). % 10.94/10.90 c_Complex_OIm(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 c_Complex_ORe(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.90 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 exists B_n0 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_n0,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 exists B_n0 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_n0,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oone__class_Oone(T_a)=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))). % 10.94/10.90 all V_x V_y T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y)=c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))). % 10.94/10.90 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))))). % 10.94/10.90 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.90 all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)). % 10.94/10.90 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2)). % 10.94/10.90 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)). % 10.94/10.90 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2). % 10.94/10.90 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)). % 10.94/10.90 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))). % 10.94/10.90 all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)). % 10.94/10.90 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_w V_v (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)). % 10.94/10.90 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z). % 10.94/10.90 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)&V_z_2!=V_w_2). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)). % 10.94/10.90 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))). % 10.94/10.90 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))). % 10.94/10.90 all V_z V_z_H V_w V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)))). % 10.94/10.90 all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))). % 10.94/10.90 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))). % 10.94/10.90 all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)). % 10.94/10.90 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)->V_z=V_w)). % 10.94/10.90 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k))). % 10.94/10.90 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)). % 10.94/10.90 all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w). % 10.94/10.90 c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls). % 10.94/10.90 all V_v_2 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls)). % 10.94/10.90 all V_v_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls)). % 10.94/10.90 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.90 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls). % 10.94/10.90 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.90 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)). % 10.94/10.90 all V_v_H_2 V_v_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))<-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2))&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)). % 10.94/10.90 all V_v_H V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H))))). % 10.94/10.90 all V_v_H_2 V_v_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))<-> (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,V_v_H_2)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls))). % 10.94/10.90 all V_v_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2)). % 10.94/10.90 c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)). % 10.94/10.90 all V_v (c_Complex_OIm(c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_v))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_v (c_Complex_ORe(c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_v))=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v)). % 10.94/10.90 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))). % 10.94/10.90 all V_w_2 V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)<->V_a_2=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))). % 10.94/10.90 all V_c V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c))))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))). % 10.94/10.90 all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))). % 10.94/10.90 all T_a (class_Int_Onumber__ring(T_a)->c_Groups_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)). % 10.94/10.90 all V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))). % 10.94/10.90 all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))). % 10.94/10.90 all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))). % 10.94/10.90 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))->V_x=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_x=c_Groups_Oone__class_Oone(tc_Int_Oint))). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 all V_n (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n)))&c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n)))). % 10.94/10.90 all V_k (c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k)=V_k). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)))). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.90 -((exists B_N1 all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_N1,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))-> (all B_N2 (-(all B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_N2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))). % 10.94/10.90 all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))). % 10.94/10.90 all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)))). % 10.94/10.90 c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). % 10.94/10.90 c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 10.94/10.90 all V_w (c_Complex_Oii!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w)). % 10.94/10.90 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))). % 10.94/10.90 c_Complex_ORe(c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 all V_n (c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)). % 10.94/10.90 c_Complex_OIm(c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.90 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.90 c_Int_Osucc(c_Int_OPls)=c_Int_OBit1(c_Int_OPls). % 10.94/10.90 all V_k (c_Int_Osucc(c_Int_OBit1(V_k))=c_Int_OBit0(c_Int_Osucc(V_k))). % 10.94/10.90 all V_k (c_Int_Osucc(c_Int_OBit0(V_k))=c_Int_OBit1(V_k)). % 10.94/10.90 all V_k (c_Int_Osucc(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2)=c_Complex_Oii<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_ya_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 all V_k T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k))). % 10.94/10.90 all V_l V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l))=c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l)))). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)))). % 10.94/10.90 all V_x V_n (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)))). % 10.94/10.90 all V_xa_2 V_na_2 (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2))))). % 10.94/10.90 all V_v ((c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v,c_Int_OPls)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v)))). % 10.94/10.90 -c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 -c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.90 all V_v_2 (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))<->c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_x (c_Int_Osucc(c_Int_Opred(V_x))=V_x). % 10.94/10.90 all V_xa_2 (-c_Nat__Numeral_Oneg(V_xa_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_xa_2)). % 10.94/10.90 all V_Z_2 (c_Nat__Numeral_Oneg(V_Z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_Z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_w_2 (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_w_2)))<->c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2))). % 10.94/10.90 -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). % 10.94/10.90 all V_w_2 (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w_2)))<->c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2))). % 10.94/10.90 all V_k (c_Int_Opred(c_Int_OBit1(V_k))=c_Int_OBit0(V_k)). % 10.94/10.90 all V_k (c_Int_Opred(c_Int_OBit0(V_k))=c_Int_OBit1(c_Int_Opred(V_k))). % 10.94/10.90 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2)). % 10.94/10.90 all V_k (c_Int_Opred(V_k)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint))). % 10.94/10.90 all V_v (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))->c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_l V_k (c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l))=c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Opred(V_k),V_l))). % 10.94/10.90 all V_v_H_2 V_v_2 (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)<-> (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))& (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))-> (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))->c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))->V_v_2=V_v_H_2))). % 10.94/10.90 all V_k V_v_H V_v ((c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))& (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))-> (c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_k))& (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)),V_k)))). % 10.94/10.90 all V_x V_n (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)))). % 10.94/10.90 all V_xa_2 V_na_2 (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2),c_RComplete_Onatfloor(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2),V_xa_2)))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))). % 10.94/10.90 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))). % 10.94/10.90 all V_n (c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)). % 10.94/10.90 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2)). % 10.94/10.90 all V_x V_y ((c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))& (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))). % 10.94/10.90 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)). % 10.94/10.90 all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 10.94/10.90 all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n). % 10.94/10.90 all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n). % 10.94/10.90 all V_m_2 V_na_2 (c_RealDef_Oreal(tc_Nat_Onat,V_na_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)<->V_na_2=V_m_2). % 10.94/10.90 all V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x)). % 10.94/10.90 c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). % 10.94/10.90 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 all V_na_2 (c_RealDef_Oreal(tc_Nat_Onat,V_na_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.90 all V_m_2 V_na_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)). % 10.94/10.90 all V_m_2 V_na_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2)). % 10.94/10.90 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 10.94/10.90 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))). % 10.94/10.90 all V_na_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)). % 10.94/10.90 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))). % 10.94/10.90 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)). % 10.94/10.90 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls). % 10.94/10.90 all V_na_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_na_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)). % 10.94/10.90 all V_m_2 V_na_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))). % 10.94/10.90 all V_m_2 V_na_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))). % 10.94/10.90 all V_a_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2))). % 10.94/10.90 all V_a_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)). % 10.94/10.90 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))). % 10.94/10.90 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)))). % 10.94/10.90 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))). % 10.94/10.90 all V_v ((c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))->c_RealDef_Oreal(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (-c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))->c_RealDef_Oreal(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v))). % 10.94/10.90 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)). % 10.94/10.90 all V_x V_y (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)). % 10.94/10.90 all V_n V_z (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))). % 10.94/10.90 all V_x V_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)). % 10.94/10.90 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)). % 10.94/10.90 all V_r (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)-> (exists B_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))))). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)->c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y)))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y))). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<->V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_n V_x (V_x=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))->c_RComplete_Onatfloor(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_n))=c_Power_Opower__class_Opower(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)). % 10.94/10.90 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n)). % 10.94/10.90 all V_n V_m (c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n)=c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n))). % 10.94/10.90 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x). % 10.94/10.90 all V_n V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n)). % 10.94/10.90 all V_n V_x T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n))). % 10.94/10.90 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all V_na_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))<->V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)). % 10.94/10.90 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n))). % 10.94/10.90 all V_w_2 V_a_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.90 all V_x V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x))). % 10.94/10.90 all V_w_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))<->c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)). % 10.94/10.90 all V_n V_x c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),V_n)). % 10.94/10.90 all V_w T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w))=c_Groups_Oone__class_Oone(T_a))& (c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w))=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_na_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_xa_2),V_na_2))<->V_xa_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_x V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))). % 10.94/10.90 all V_a_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all T_a (class_Rings_Osemiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all T_a (class_Rings_Osemiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all V_x V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all V_y V_x T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->V_x=V_y)))). % 10.94/10.90 all V_y V_x T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__idom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)). % 10.94/10.90 all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)). % 10.94/10.90 all V_y V_x T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))). % 10.94/10.90 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a). % 10.94/10.90 all V_k V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))). % 10.94/10.90 all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.90 all V_a T_a (class_Divides_Osemiring__div(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))). % 10.94/10.90 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.90 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.90 all V_k V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)))). % 10.94/10.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m))). % 10.94/10.90 all V_m (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_m). % 10.94/10.90 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)))))). % 10.94/10.90 all V_m V_n V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))))). % 10.94/10.90 all V_w V_v (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))). % 10.94/10.90 all V_a (V_a!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.90 all V_b (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). % 10.94/10.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2))). % 10.94/10.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). % 10.94/10.90 all V_k_2 V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)). % 10.94/10.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2))). % 10.94/10.90 all V_i_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_i_2))). % 10.94/10.90 all V_b_2 V_a_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2,V_a_2)&c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2))). % 10.94/10.90 all V_b V_b_H V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). % 10.94/10.90 all V_b V_b_H V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))). % 10.94/10.90 all V_b V_a_H V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,V_a_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)))). % 10.94/10.90 all V_b V_a_H V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,V_a_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))). % 10.94/10.90 all V_k V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x))). % 10.94/10.90 all V_v V_w ((c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)))& (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Power_Opower__class_Opower(T_a,V_a,V_n)!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_n T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n)=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all V_n V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n)=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)). % 10.94/10.90 all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a). % 10.94/10.90 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)))). % 10.94/10.90 all V_na_2 V_a_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.90 all V_na_2 V_m_2 V_a_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)-> (c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2)=c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)<->V_m_2=V_na_2))). % 10.94/10.90 all V_n V_a V_b T_a (class_Fields_Ofield(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n)=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)))). % 10.94/10.90 all V_a T_a (class_Power_Opower(T_a)->c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)). % 10.94/10.90 all V_n V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n)). % 10.94/10.90 all V_na_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.90 all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))). % 10.94/10.90 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.90 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n))). % 10.94/10.90 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))))). % 10.94/10.90 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))). % 10.94/10.90 all V_ya_2 V_xa_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)))). % 10.94/10.90 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))))). % 10.94/10.90 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))). % 10.94/10.90 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Power_Opower__class_Opower(T_a,V_a,V_n)=c_Power_Opower__class_Opower(T_a,V_b,V_n)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_a=V_b))))). % 10.94/10.90 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)))))). % 10.94/10.90 all V_ya_2 V_xa_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_ya_2)))). % 10.94/10.90 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)))). % 10.94/10.90 all V_z (c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_z). % 10.94/10.90 all V_y V_x V_u (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)))))). % 10.94/10.90 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 all V_xa_2 (c_NthRoot_Osqrt(V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_NthRoot_Osqrt(V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.90 all V_ya_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_NthRoot_Osqrt(V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))). % 10.94/10.90 all V_ya_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)). % 10.94/10.90 all V_ya_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2)). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x))). % 10.94/10.90 all V_ya_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2)). % 10.94/10.90 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.90 all V_ya_2 V_xa_2 (c_NthRoot_Osqrt(V_xa_2)=c_NthRoot_Osqrt(V_ya_2)<->V_xa_2=V_ya_2). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))). % 10.94/10.90 all V_y V_x (c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))). % 10.94/10.90 c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.90 all V_xa_2 (c_NthRoot_Osqrt(V_xa_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.90 all V_k V_x (c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),V_k)). % 10.94/10.90 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.90 all V_x (c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)). % 10.94/10.90 all V_xa_2 (c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_xa_2<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_x). % 10.94/10.90 all V_x V_y (c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_x-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_NthRoot_Osqrt(V_x)=V_y)). % 10.94/10.90 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.90 all V_u (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u)). % 10.94/10.90 all V_d V_b V_c V_a c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))). % 10.94/10.90 all V_x V_y c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_y V_x (c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))=V_y->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_y V_x (c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))=V_x->V_y=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_x V_y c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_y V_x (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y))=c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.90 all V_y V_u V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u))). % 10.94/10.90 all V_ya V_xa V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))). % 10.94/10.90 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_b)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_a))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_b,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a)). % 10.94/10.90 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))). % 10.94/10.90 all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))). % 10.94/10.90 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Groups_Ozero__class_Ozero(T_a))& (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))). % 10.94/10.90 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b)=V_a)). % 10.94/10.90 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b)=V_a)). % 10.94/10.90 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))). % 10.94/10.90 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))). % 10.94/10.90 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))). % 10.94/10.90 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))). % 10.94/10.90 all V_y V_x (c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y))). % 10.94/10.90 all V_x (c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)). % 10.94/10.90 all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q))). % 10.94/10.90 all V_ya_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_b_2 V_a_2 V_fa_2 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_a_2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_b_2))). % 10.94/10.90 all V_n V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n))=c_Groups_Oone__class_Oone(tc_Int_Oint)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.90 all V_z V_y V_x (c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.90 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a))). % 10.94/10.90 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))). % 10.94/10.90 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))). % 10.94/10.90 all V_b_2 V_c_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d))))). % 10.94/10.90 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n))))). % 10.94/10.90 all V_c V_b V_v T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))). % 10.94/10.90 all V_v V_b V_a T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))). % 10.94/10.90 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b))). % 10.94/10.90 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))). % 10.94/10.90 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)<->V_c_2=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2))). % 10.94/10.90 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2)=V_d_2)). % 10.94/10.90 all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)). % 10.94/10.90 all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m)). % 10.94/10.90 all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m)). % 10.94/10.90 all V_c V_b V_v T_b (class_Int_Onumber(T_b)&class_Rings_Oring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))). % 10.94/10.90 all V_v V_b V_a T_b (class_Int_Onumber(T_b)&class_Rings_Oring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)<->c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)=V_b_2))). % 10.94/10.90 all V_a_2 V_b_2 V_c_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2<->V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)))). % 10.94/10.90 all V_a V_b V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b=c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)->c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a))). % 10.94/10.90 all V_b V_a V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)=V_b->V_a=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))). % 10.94/10.90 all V_c_2 V_b_2 V_a_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)=V_b_2)& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_a_2 V_c_2 V_b_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))). % 10.94/10.90 all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))). % 10.94/10.90 all V_w_2 V_xa_2 V_z_2 V_ya_2 T_a (class_Fields_Ofield(T_a)-> (V_ya_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2)=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)<->c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2)=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2))))). % 10.94/10.90 all V_z (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z)=V_z). % 10.94/10.90 all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a). % 10.94/10.90 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a). % 10.94/10.90 all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a). % 10.94/10.90 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a). % 10.94/10.90 all V_z V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z)). % 10.94/10.90 all V_w V_v (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))). % 10.94/10.90 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))). % 10.94/10.90 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))). % 10.94/10.90 all V_z (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)=V_z). % 10.94/10.90 all V_z (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z). % 10.94/10.90 all V_a V_r (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r)). % 10.94/10.90 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)). % 10.94/10.90 all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 10.94/10.90 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry))). % 10.94/10.90 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry))). % 10.94/10.90 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)))). % 10.94/10.90 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly)). % 10.94/10.90 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx))). % 10.94/10.90 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry)). % 10.94/10.90 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)). % 10.94/10.90 all V_z3 V_z2 V_z1 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3))). % 10.94/10.90 all V_w V_z (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z)). % 10.94/10.90 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))). % 10.94/10.90 all V_z3 V_z2 V_z1 (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_z3))). % 10.94/10.90 all V_w V_z (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w)=c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z)). % 10.94/10.90 all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 10.94/10.90 all V_w V_z2 V_z1 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w))). % 10.94/10.90 all V_l V_k (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k),V_l)=c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l))). % 10.94/10.90 all V_w (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,V_w)=c_Int_OPls). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)). % 10.94/10.90 all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z))). % 10.94/10.90 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_a_2!=V_b_2&V_c_2!=V_d_2<->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)))). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))). % 10.94/10.90 all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m)). % 10.94/10.90 all V_z_2 V_xa_2 V_ya_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_ya_2))<->V_w_2=V_xa_2|V_ya_2=V_z_2)). % 10.94/10.90 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))). % 10.94/10.90 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))). % 10.94/10.90 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))). % 10.94/10.90 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))). % 10.94/10.90 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c)). % 10.94/10.90 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))). % 10.94/10.90 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))). % 10.94/10.90 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s))))). % 10.94/10.90 all V_z2 V_z1 V_w (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))). % 10.94/10.90 all V_w V_z2 V_z1 (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))). % 10.94/10.90 all V_w V_z V_y V_x T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w))). % 10.94/10.90 all V_w V_z2 V_z1 (c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))). % 10.94/10.90 all V_z2 V_z1 V_w (c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))). % 10.94/10.90 all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.90 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.90 all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.90 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))). % 10.94/10.90 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))). % 10.94/10.90 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))). % 10.94/10.90 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)<->V_a_2=V_b_2)). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)<->V_a_2=V_b_2)). % 10.94/10.90 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j)))). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)))). % 10.94/10.90 all V_xa_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2))<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.90 all V_y V_x V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)))). % 10.94/10.90 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)))). % 10.94/10.90 all V_ya_2 V_xa_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2))). % 10.94/10.90 all V_d V_b V_c V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d))))). % 10.94/10.90 all V_n V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)))). % 10.94/10.90 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.90 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.91 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.91 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))). % 10.94/10.91 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.91 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.91 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.91 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))). % 10.94/10.91 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))). % 10.94/10.91 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))). % 10.94/10.91 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)))). % 10.94/10.91 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.91 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.91 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)))<->V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a))). % 10.94/10.91 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x))))). % 10.94/10.91 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x))))). % 10.94/10.91 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)))). % 10.94/10.91 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2))). % 10.94/10.91 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2))). % 10.94/10.91 all V_d_2 V_b_2 V_c_2 V_ea_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)))). % 10.94/10.91 all V_c_2 V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))))). % 10.94/10.91 all V_a_2 V_c_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))))). % 10.94/10.91 all V_b_2 V_a_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)))). % 10.94/10.91 all V_a_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))))). % 10.94/10.91 all V_z V_x V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)))). % 10.94/10.91 all V_x V_z V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)->c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))). % 10.94/10.91 all V_b_2 V_a_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))))). % 10.94/10.91 all V_a_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)))). % 10.94/10.91 all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))). % 10.94/10.91 all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))). % 10.94/10.91 all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.91 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_y),V_x)=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x)))). % 10.94/10.91 all V_b V_a T_a (class_Rings_Oordered__ring__abs(T_a)-> ((c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))& (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)))->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))). % 10.94/10.91 all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z))))). % 10.94/10.91 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z))). % 10.94/10.91 all V_z V_x V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y))). % 10.94/10.91 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z))). % 10.94/10.91 all V_x V_z V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y))). % 10.94/10.91 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))))). % 10.94/10.91 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))))). % 10.94/10.91 all V_a_2 V_w_2 V_b_2 T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_a_2<-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))& (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.91 all V_w_2 V_c_2 V_b_2 T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2))& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.91 all V_c_2 V_b_2 V_w_2 T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)=V_b_2)& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.91 all V_w_2 V_b_2 V_a_2 T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))<-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_b_2)& (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))). % 10.94/10.91 all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z))))). % 10.94/10.91 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z))). % 10.94/10.91 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z))). % 10.94/10.91 all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))). % 10.94/10.91 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))). % 10.94/10.91 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))). % 10.94/10.91 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))). % 10.94/10.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__semiring__strict(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint). % 10.94/10.91 class_Groups_Olinordered__ab__group__add(tc_Int_Oint). % 10.94/10.91 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint). % 10.94/10.91 class_Rings_Oordered__cancel__semiring(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__ring__strict(tc_Int_Oint). % 10.94/10.91 class_Rings_Oring__no__zero__divisors(tc_Int_Oint). % 10.94/10.91 class_Rings_Oordered__comm__semiring(tc_Int_Oint). % 10.94/10.91 class_Groups_Oordered__ab__group__add(tc_Int_Oint). % 10.94/10.91 class_Groups_Ocancel__semigroup__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__semiring(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__semidom(tc_Int_Oint). % 10.94/10.91 class_Groups_Oab__semigroup__mult(tc_Int_Oint). % 10.94/10.91 class_Groups_Ocomm__monoid__mult(tc_Int_Oint). % 10.94/10.91 class_Groups_Oab__semigroup__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Oordered__semiring(tc_Int_Oint). % 10.94/10.91 class_Rings_Oordered__ring__abs(tc_Int_Oint). % 10.94/10.91 class_Rings_Ono__zero__divisors(tc_Int_Oint). % 10.94/10.91 class_Groups_Ocomm__monoid__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__ring(tc_Int_Oint). % 10.94/10.91 class_Rings_Olinordered__idom(tc_Int_Oint). % 10.94/10.91 class_Rings_Ocomm__semiring__1(tc_Int_Oint). % 10.94/10.91 class_Divides_Osemiring__div(tc_Int_Oint). % 10.94/10.91 class_Rings_Ocomm__semiring(tc_Int_Oint). % 10.94/10.91 class_Groups_Oab__group__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Ozero__ne_q__one(tc_Int_Oint). % 10.94/10.91 class_Rings_Oordered__ring(tc_Int_Oint). % 10.94/10.91 class_Orderings_Opreorder(tc_Int_Oint). % 10.94/10.91 class_Orderings_Olinorder(tc_Int_Oint). % 10.94/10.91 class_Groups_Omonoid__mult(tc_Int_Oint). % 10.94/10.91 class_Groups_Omonoid__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Osemiring__1(tc_Int_Oint). % 10.94/10.91 class_Rings_Osemiring__0(tc_Int_Oint). % 10.94/10.91 class_Groups_Ogroup__add(tc_Int_Oint). % 10.94/10.91 class_Rings_Omult__zero(tc_Int_Oint). % 10.94/10.91 class_Orderings_Oorder(tc_Int_Oint). % 10.94/10.91 class_Int_Oring__char__0(tc_Int_Oint). % 10.94/10.91 class_Int_Onumber__ring(tc_Int_Oint). % 10.94/10.91 class_Rings_Osemiring(tc_Int_Oint). % 10.94/10.91 class_Orderings_Oord(tc_Int_Oint). % 10.94/10.91 class_Rings_Oring__1(tc_Int_Oint). % 10.94/10.91 class_Power_Opower(tc_Int_Oint). % 10.94/10.91 class_Groups_Ozero(tc_Int_Oint). % 10.94/10.91 class_Rings_Oring(tc_Int_Oint). % 10.94/10.91 class_Int_Onumber(tc_Int_Oint). % 10.94/10.91 class_Groups_Oone(tc_Int_Oint). % 10.94/10.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat). % 10.94/10.91 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat). % 10.94/10.91 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat). % 10.94/10.91 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat). % 10.94/10.91 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat). % 10.94/10.91 class_Rings_Oordered__comm__semiring(tc_Nat_Onat). % 10.94/10.91 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat). % 10.94/10.91 class_Rings_Olinordered__semiring(tc_Nat_Onat). % 10.94/10.91 class_Rings_Olinordered__semidom(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oab__semigroup__mult(tc_Nat_Onat). % 10.94/10.91 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oab__semigroup__add(tc_Nat_Onat). % 10.94/10.91 class_Rings_Oordered__semiring(tc_Nat_Onat). % 10.94/10.91 class_Rings_Ono__zero__divisors(tc_Nat_Onat). % 10.94/10.91 class_Groups_Ocomm__monoid__add(tc_Nat_Onat). % 10.94/10.91 class_Rings_Ocomm__semiring__1(tc_Nat_Onat). % 10.94/10.91 class_Divides_Osemiring__div(tc_Nat_Onat). % 10.94/10.91 class_Rings_Ocomm__semiring(tc_Nat_Onat). % 10.94/10.91 class_Rings_Ozero__ne_q__one(tc_Nat_Onat). % 10.94/10.91 class_Orderings_Opreorder(tc_Nat_Onat). % 10.94/10.91 class_Orderings_Olinorder(tc_Nat_Onat). % 10.94/10.91 class_Groups_Omonoid__mult(tc_Nat_Onat). % 10.94/10.91 class_Groups_Omonoid__add(tc_Nat_Onat). % 10.94/10.91 class_Rings_Osemiring__1(tc_Nat_Onat). % 10.94/10.91 class_Rings_Osemiring__0(tc_Nat_Onat). % 10.94/10.91 class_Rings_Omult__zero(tc_Nat_Onat). % 10.94/10.91 class_Orderings_Oorder(tc_Nat_Onat). % 10.94/10.91 class_Rings_Osemiring(tc_Nat_Onat). % 10.94/10.91 class_Orderings_Oord(tc_Nat_Onat). % 10.94/10.91 class_Power_Opower(tc_Nat_Onat). % 10.94/10.91 class_Groups_Ozero(tc_Nat_Onat). % 10.94/10.91 class_Int_Onumber(tc_Nat_Onat). % 10.94/10.91 class_Groups_Oone(tc_Nat_Onat). % 10.94/10.91 class_Orderings_Opreorder(tc_HOL_Obool). % 10.94/10.91 class_Orderings_Oorder(tc_HOL_Obool). % 10.94/10.91 class_Orderings_Oord(tc_HOL_Obool). % 10.94/10.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal). % 10.94/10.91 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal). % 10.94/10.91 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal). % 10.94/10.91 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal). % 10.94/10.91 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal). % 10.94/10.91 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal). % 10.94/10.91 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__semiring(tc_RealDef_Oreal). % 10.94/10.91 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__semidom(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal). % 10.94/10.91 class_Fields_Olinordered__field(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oordered__semiring(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__ring(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Olinordered__idom(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Odivision__ring(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Ocomm__semiring(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Oab__group__add(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal). % 10.94/10.91 class_Rings_Oordered__ring(tc_RealDef_Oreal). % 10.94/10.91 class_Orderings_Opreorder(tc_RealDef_Oreal). % 10.94/10.91 class_Orderings_Olinorder(tc_RealDef_Oreal). % 10.94/10.91 class_Groups_Omonoid__mult(tc_RealDef_Oreal). % 10.94/10.92 class_Groups_Omonoid__add(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Osemiring__1(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Osemiring__0(tc_RealDef_Oreal). % 10.94/10.92 class_Groups_Ogroup__add(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Omult__zero(tc_RealDef_Oreal). % 10.94/10.92 class_Orderings_Oorder(tc_RealDef_Oreal). % 10.94/10.92 class_Int_Oring__char__0(tc_RealDef_Oreal). % 10.94/10.92 class_Int_Onumber__ring(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Osemiring(tc_RealDef_Oreal). % 10.94/10.92 class_Orderings_Oord(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Oring__1(tc_RealDef_Oreal). % 10.94/10.92 class_Fields_Ofield(tc_RealDef_Oreal). % 10.94/10.92 class_Power_Opower(tc_RealDef_Oreal). % 10.94/10.92 class_Groups_Ozero(tc_RealDef_Oreal). % 10.94/10.92 class_Rings_Oring(tc_RealDef_Oreal). % 10.94/10.92 class_Int_Onumber(tc_RealDef_Oreal). % 10.94/10.92 class_Groups_Oone(tc_RealDef_Oreal). % 10.94/10.92 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex). % 10.94/10.92 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex). % 10.94/10.92 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex). % 10.94/10.92 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex). % 10.94/10.92 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex). % 10.94/10.92 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Odivision__ring(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Oab__group__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Omonoid__mult(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Omonoid__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Osemiring__1(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Osemiring__0(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ogroup__add(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Omult__zero(tc_Complex_Ocomplex). % 10.94/10.92 class_Int_Oring__char__0(tc_Complex_Ocomplex). % 10.94/10.92 class_Int_Onumber__ring(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Osemiring(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Oring__1(tc_Complex_Ocomplex). % 10.94/10.92 class_Fields_Ofield(tc_Complex_Ocomplex). % 10.94/10.92 class_Power_Opower(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Ozero(tc_Complex_Ocomplex). % 10.94/10.92 class_Rings_Oring(tc_Complex_Ocomplex). % 10.94/10.92 class_Int_Onumber(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Oone(tc_Complex_Ocomplex). % 10.94/10.92 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Ozero__ne_q__one(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Power_Opower(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral). % 10.94/10.92 -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____). % 10.94/10.92 end_of_list. % 10.94/10.92 % 10.94/10.92 -------> usable clausifies to: % 10.94/10.92 % 10.94/10.92 list(usable). % 10.94/10.92 0 [] A=A. % 10.94/10.92 0 [] hAPP(V_fa_2,$f1(V_gb_2,V_fa_2))!=hAPP(V_gb_2,$f1(V_gb_2,V_fa_2))|V_fa_2=V_gb_2. % 10.94/10.92 0 [] c_SEQ_Osubse_q(v_f____). % 10.94/10.92 0 [] c_SEQ_Osubse_q(v_ga____). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e____). % 10.94/10.92 0 [] c_SEQ_Osubse_q(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_s(B_n)),v_r). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N1____,hAPP(v_ga____,v_n____)). % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2=V_real1_H_2. % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real2_2=V_real2_H_2. % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2!=V_real1_H_2|V_real2_2!=V_real2_H_2. % 10.94/10.92 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2). % 10.94/10.92 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_xa_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)). % 10.94/10.92 0 [] hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))!=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))|hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_xa_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2). % 10.94/10.92 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=V_c_2|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2). % 10.94/10.92 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2)). % 10.94/10.92 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N2____,v_n____). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_xa_2|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_xa_2|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_xa_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2). % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2. % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2. % 10.94/10.92 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a. % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_xa_2))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_xa_2))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)). % 10.94/10.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2!=V_b_2|V_c_2=V_d_2. % 10.94/10.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2=V_b_2|V_c_2!=V_d_2. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_s(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),v_r). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),v_n____). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x). % 10.94/10.92 0 [] c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2). % 10.94/10.92 0 [] c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2). % 10.94/10.92 0 [] -c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,hAPP(V_fa_2,V_na_2)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 10.94/10.92 0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)). % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)|V_b_2=V_c_2. % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)|V_b_2!=V_c_2. % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)!=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)|V_b_2=V_c_2. % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)|V_b_2!=V_c_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)). % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c. % 10.94/10.92 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c. % 10.94/10.92 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c. % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)). % 10.94/10.92 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a. % 10.94/10.92 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a. % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a. % 10.94/10.92 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a. % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 10.94/10.92 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)). % 10.94/10.92 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a. % 10.94/10.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 10.94/10.92 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)). % 10.94/10.92 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))). % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)). % 10.94/10.92 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y. % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a). % 10.94/10.92 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a). % 10.94/10.92 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_gb_2,V_xa_2)). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_xa_2=V_ya_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x),hAPP(V_gb_2,B_x)). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,$f2(V_gb_2,V_fa_2,T_a,T_b)),hAPP(V_gb_2,$f2(V_gb_2,V_fa_2,T_a,T_b))). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2=V_ya_2|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y. % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x. % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a). % 10.94/10.92 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w). % 10.94/10.92 0 [] -c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)). % 10.94/10.92 0 [] c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f4(V_fa_2),$f3(V_fa_2)). % 10.94/10.92 0 [] c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f4(V_fa_2)),hAPP(V_fa_2,$f3(V_fa_2))). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y). % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y. % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a). % 10.94/10.92 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.92 0 [] c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f5(V_b_2,V_a_2,V_P_2)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f5(V_b_2,V_a_2,V_P_2))). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f5(V_b_2,V_a_2,V_P_2)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f5(V_b_2,V_a_2,V_P_2))). % 10.94/10.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 10.94/10.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f6(V_b_2,V_a_2,V_P_2)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f6(V_b_2,V_a_2,V_P_2))). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f6(V_b_2,V_a_2,V_P_2)). % 10.94/10.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f6(V_b_2,V_a_2,V_P_2))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2). % 10.94/10.92 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_gb_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2,V_gb_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2,V_fa_2). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n. % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m. % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2=V_na_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n). % 10.94/10.92 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x). % 10.94/10.92 0 [] V_m_2=V_na_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.92 0 [] V_m_2!=V_na_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] V_m_2!=V_na_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2)|V_m_2=V_na_2. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2)|V_m_2!=V_na_2. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_na_2,V_k_2)|V_m_2=V_na_2. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_na_2,V_k_2)|V_m_2!=V_na_2. % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m. % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m). % 10.94/10.92 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2)|V_m_2=V_na_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2)|V_m_2!=V_na_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.92 0 [] V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_na_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_na_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_na_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2!=V_na_2. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2=V_na_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2=V_na_2. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)|V_m_2!=V_na_2. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_na_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_na_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)|V_na_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f7(V_na_2,V_m_2)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2)|V_na_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_na_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m. % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(v_f____,hAPP(v_ga____,v_n____))),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),c_Complex_ORe(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),c_Complex_OIm(c_Complex_Ocomplex_OComplex(v_x____,v_y____)))))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,$f8(V_l_2,V_k_2)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f10(V_X_2,T_a),$f9(V_X_2,T_a)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f9(V_X_2,T_a)),hAPP(V_X_2,$f10(V_X_2,T_a))). % 10.94/10.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a. % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a. % 10.94/10.92 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f11(V_X_2,T_a)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f11(V_X_2,T_a)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f12(V_X_2,T_a,B_K))),B_K). % 10.94/10.92 0 [] c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z))=V_z. % 10.94/10.92 0 [] c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a). % 10.94/10.92 0 [] V_xa_2!=V_ya_2|c_Complex_ORe(V_xa_2)=c_Complex_ORe(V_ya_2). % 10.94/10.92 0 [] V_xa_2!=V_ya_2|c_Complex_OIm(V_xa_2)=c_Complex_OIm(V_ya_2). % 10.94/10.92 0 [] V_xa_2=V_ya_2|c_Complex_ORe(V_xa_2)!=c_Complex_ORe(V_ya_2)|c_Complex_OIm(V_xa_2)!=c_Complex_OIm(V_ya_2). % 10.94/10.92 0 [] c_Complex_ORe(V_x)!=c_Complex_ORe(V_y)|c_Complex_OIm(V_x)!=c_Complex_OIm(V_y)|V_x=V_y. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y))). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)). % 10.94/10.92 0 [] c_Complex_OIm(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)). % 10.94/10.92 0 [] c_Complex_ORe(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a). % 10.94/10.92 0 [] c_Complex_OIm(c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y. % 10.94/10.92 0 [] c_Complex_ORe(c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x. % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y))))). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a. % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a. % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)). % 10.94/10.92 0 [] c_Complex_OIm(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] c_Complex_ORe(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.92 0 [] c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(V_x),c_Complex_OIm(V_y)). % 10.94/10.92 0 [] c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(V_x),c_Complex_ORe(V_y)). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))). % 10.94/10.92 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)). % 10.94/10.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f13(B_r),B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),B_r). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f14(B_r),B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),B_r). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(v_s(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_xa_2). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_ra_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_xa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f15(V_X_2,V_K_2,T_a))),V_K_2)|c_SEQ_OBse_q(T_a,V_X_2). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f16(V_X_2,T_a)). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f16(V_X_2,T_a)). % 10.94/10.92 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_xa_2|V_xa_2=c_Groups_Oone__class_Oone(T_a). % 10.94/10.92 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_xa_2|V_xa_2!=c_Groups_Oone__class_Oone(T_a). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.92 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a). % 10.94/10.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.92 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))). % 10.94/10.92 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,$f17(V_X_2,V_M_2,T_a,T_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,$f17(V_X_2,V_M_2,T_a,T_b)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f18(V_b,V_x,V_a)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f18(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_a,B_y). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f18(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_y,V_b). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_x____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,v_n____)))),v_y____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(V_X_2,T_a),$f19(V_X_2,T_a)). % 10.94/10.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f20(V_X_2,T_a)),hAPP(V_X_2,$f19(V_X_2,T_a))). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2,$f21(V_K_2,V_X_2,V_N_2,T_a))|c_SEQ_OBse_q(T_a,V_X_2). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f21(V_K_2,V_X_2,V_N_2,T_a))),V_K_2)|c_SEQ_OBse_q(T_a,V_X_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f22(V_b,V_x,V_a)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f22(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),$f22(V_b,V_x,V_a))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N1____,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N2____,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=V_x. % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)). % 10.94/10.92 0 [] c_Int_OBit1(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k). % 10.94/10.92 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_RealVector_Oreal__normed__field(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OPls). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,c_Int_OPls). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__field(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)). % 10.94/10.92 0 [] c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OPls). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls)=V_k. % 10.94/10.92 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l))=c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l))=c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Int_OBit0(c_Int_OPls)=c_Int_OPls. % 10.94/10.92 0 [] c_Int_OPls!=c_Int_OBit1(V_l). % 10.94/10.92 0 [] c_Int_OPls!=c_Int_OBit0(V_l_2)|c_Int_OPls=V_l_2. % 10.94/10.92 0 [] c_Int_OPls=c_Int_OBit0(V_l_2)|c_Int_OPls!=V_l_2. % 10.94/10.92 0 [] -class_Fields_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_a. % 10.94/10.92 0 [] -class_Fields_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_x. % 10.94/10.92 0 [] c_Int_OBit1(V_k)!=c_Int_OPls. % 10.94/10.92 0 [] c_Int_OBit0(V_k_2)!=c_Int_OPls|V_k_2=c_Int_OPls. % 10.94/10.92 0 [] c_Int_OBit0(V_k_2)=c_Int_OPls|V_k_2!=c_Int_OPls. % 10.94/10.92 0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=V_xa_2|V_xa_2=c_Int_Onumber__class_Onumber__of(T_a,V_w_2). % 10.94/10.92 0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=V_xa_2|V_xa_2!=c_Int_Onumber__class_Onumber__of(T_a,V_w_2). % 10.94/10.92 0 [] c_Int_OBit0(V_k)!=c_Int_OBit1(V_l). % 10.94/10.92 0 [] c_Int_OBit1(V_k)!=c_Int_OBit0(V_l). % 10.94/10.92 0 [] c_Int_OBit0(V_k_2)!=c_Int_OBit0(V_l_2)|V_k_2=V_l_2. % 10.94/10.92 0 [] c_Int_OBit0(V_k_2)=c_Int_OBit0(V_l_2)|V_k_2!=V_l_2. % 10.94/10.92 0 [] c_Int_OBit1(V_k_2)!=c_Int_OBit1(V_l_2)|V_k_2=V_l_2. % 10.94/10.92 0 [] c_Int_OBit1(V_k_2)=c_Int_OBit1(V_l_2)|V_k_2!=V_l_2. % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.92 0 [] c_Int_OBit0(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k)=V_k. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls)=V_k. % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))=V_a. % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a)=V_a. % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l))=c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l))=c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l))=c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.92 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls). % 10.94/10.92 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2). % 10.94/10.92 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls). % 10.94/10.92 0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.92 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)). % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)). % 10.94/10.93 0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)). % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a. % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)). % 10.94/10.93 0 [] -class_Int_Onumber(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)). % 10.94/10.93 0 [] -class_Int_Onumber(T_a)| -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)). % 10.94/10.93 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a!=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(T_a)|V_a_2=V_b_2. % 10.94/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)=c_Groups_Oone__class_Oone(T_a)|V_a_2!=V_b_2. % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Complex_OIm(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_ORe(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c1,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B_n)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oone__class_Oone(T_a)=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y)=c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2. % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z. % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2. % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)|V_z_2=V_w_2. % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)|V_z=V_w. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.93 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,V_v_H_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,V_v_H_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v_2,c_Int_OPls). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2). % 10.94/10.93 0 [] c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)). % 10.94/10.93 0 [] c_Complex_OIm(c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_v))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_ORe(c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_v))=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)|V_a_2=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)|V_a_2!=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 10.94/10.93 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|V_x=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_x=c_Groups_Oone__class_Oone(tc_Int_Oint). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n))). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k)=V_k. % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c3,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B_n))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c4,X1)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)). % 10.94/10.93 0 [] c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex). % 10.94/10.93 0 [] c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex). % 10.94/10.93 0 [] c_Complex_Oii!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w). % 10.94/10.93 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)). % 10.94/10.93 0 [] c_Complex_ORe(c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n). % 10.94/10.93 0 [] c_Complex_OIm(c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.93 0 [] c_Int_Osucc(c_Int_OPls)=c_Int_OBit1(c_Int_OPls). % 10.94/10.93 0 [] c_Int_Osucc(c_Int_OBit1(V_k))=c_Int_OBit0(c_Int_Osucc(V_k)). % 10.94/10.93 0 [] c_Int_Osucc(c_Int_OBit0(V_k))=c_Int_OBit1(V_k). % 10.94/10.93 0 [] c_Int_Osucc(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2)!=c_Complex_Oii|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2)!=c_Complex_Oii|V_ya_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2)=c_Complex_Oii|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l))=c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_v,c_Int_OPls)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Int_Osucc(c_Int_Opred(V_x))=V_x. % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_xa_2). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_xa_2). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(V_Z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_Z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(V_Z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_Z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_w_2)))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_w_2)))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w_2)))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w_2)))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w_2)). % 10.94/10.93 0 [] c_Int_Opred(c_Int_OBit1(V_k))=c_Int_OBit0(V_k). % 10.94/10.93 0 [] c_Int_Opred(c_Int_OBit0(V_k))=c_Int_OBit1(c_Int_Opred(V_k)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2). % 10.94/10.93 0 [] c_Int_Opred(V_k)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l))=c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Opred(V_k),V_l)). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))|V_v_2=V_v_H_2. % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))|V_v_2!=V_v_H_2. % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_v_2!=V_v_H_2. % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))|V_v_2!=V_v_H_2. % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2)). % 10.94/10.93 0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_v_2!=V_v_H_2. % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_k). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)),V_k). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2),c_RComplete_Onatfloor(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2),V_xa_2). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_na_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_na_2),c_RComplete_Onatfloor(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_na_2),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 10.94/10.93 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)). % 10.94/10.93 0 [] c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n). % 10.94/10.93 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 10.94/10.93 0 [] c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n. % 10.94/10.93 0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n. % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_na_2)!=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_na_2=V_m_2. % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_na_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_na_2!=V_m_2. % 10.94/10.93 0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x). % 10.94/10.93 0 [] c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))=c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_na_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_na_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a). % 10.94/10.93 0 [] c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_na_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_na_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_na_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_na_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n). % 10.94/10.93 0 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))|c_RealDef_Oreal(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))|c_RealDef_Oreal(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f23(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,$f23(V_r))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)|c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y)))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] V_x!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))|c_RComplete_Onatfloor(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_n))=c_Power_Opower__class_Opower(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n). % 10.94/10.93 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n). % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),V_n)=c_RealDef_Oreal(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_m,V_n)). % 10.94/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x. % 10.94/10.93 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n). % 10.94/10.93 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n)). % 10.94/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),V_n)). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_xa_2),V_na_2))|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_xa_2),V_na_2))|V_xa_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_xa_2),V_na_2))|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))). % 10.94/10.93 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Osemiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Osemiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|V_x=V_y. % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_xa_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_ya_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_m. % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)). % 10.94/10.93 0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)). % 10.94/10.93 0 [] V_a=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2). % 10.94/10.93 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_i_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_i_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2,V_a_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2,V_a_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,V_a_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,V_a_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)). % 10.94/10.93 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Power_Opower__class_Opower(T_a,V_a,V_n)!=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n)=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n)=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n). % 10.94/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a. % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2)!=c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)|V_m_2=V_na_2. % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2)=c_Power_Opower__class_Opower(T_a,V_a_2,V_na_2)|V_m_2!=V_na_2. % 10.94/10.93 0 [] -class_Fields_Ofield(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n)=c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)). % 10.94/10.93 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)|V_na_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_xa_2,V_na_2))|V_na_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Oone__class_Oone(T_a). % 10.94/10.93 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Power_Opower__class_Opower(T_a,V_a,V_n)!=c_Power_Opower__class_Opower(T_a,V_b,V_n)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_a=V_b. % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_xa_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n). % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_z. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_NthRoot_Osqrt(V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_NthRoot_Osqrt(V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)!=c_NthRoot_Osqrt(V_ya_2)|V_xa_2=V_ya_2. % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)=c_NthRoot_Osqrt(V_ya_2)|V_xa_2!=V_ya_2. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_xa_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(V_xa_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),V_k). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x). % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=V_xa_2|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_xa_2| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_x. % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=V_x| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_NthRoot_Osqrt(V_x)=V_y. % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))!=V_y|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))!=V_x|V_y=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). % 10.94/10.93 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y))=c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.93 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u). % 10.94/10.93 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))). % 10.94/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_b)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_a))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_b,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a). % 10.94/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_c!=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Groups_Ozero__class_Ozero(T_a). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b)=V_a. % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b)=V_a. % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b). % 10.94/10.93 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b). % 10.94/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)). % 10.94/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)). % 10.94/10.93 0 [] c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x). % 10.94/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q)). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 10.94/10.93 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_a_2))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2)),V_b_2)). % 10.94/10.93 0 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint). % 10.94/10.93 0 [] c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 10.94/10.93 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 10.94/10.93 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Rings_Oordered__comm__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)). % 10.94/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)). % 10.94/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)). % 11.02/10.93 0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)). % 11.02/10.93 0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))). % 11.02/10.93 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))). % 11.02/10.93 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)|V_c_2=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2). % 11.02/10.93 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)|V_c_2!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2). % 11.02/10.93 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2)=V_d_2. % 11.02/10.93 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2)!=V_d_2. % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m). % 11.02/10.93 0 [] -class_Int_Onumber(T_b)| -class_Rings_Oring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)). % 11.02/10.93 0 [] -class_Int_Onumber(T_b)| -class_Rings_Oring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))). % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)=V_b_2. % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)!=V_b_2. % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_a_2|V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2). % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2). % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|V_b!=c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)|c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a. % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)!=V_b|V_a=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)=V_b_2. % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)!=V_b_2|V_c_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_a_2|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_a_2|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_a_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b). % 11.02/10.93 0 [] -class_Fields_Ofield(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a)|V_z_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)|c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2)=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2). % 11.02/10.93 0 [] -class_Fields_Ofield(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a)|V_z_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2)=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)|c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2)!=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z)=V_z. % 11.02/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a. % 11.02/10.93 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a. % 11.02/10.93 0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a. % 11.02/10.93 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a. % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a. % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a. % 11.02/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)). % 11.02/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)). % 11.02/10.93 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)=V_z. % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z. % 11.02/10.93 0 [] c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r). % 11.02/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_a). % 11.02/10.93 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_b,V_a). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z). % 11.02/10.93 0 [] -class_Groups_Oab__semigroup__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_z3)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w)=c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k),V_l)=c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,V_w)=c_Int_OPls. % 11.02/10.93 0 [] -class_Rings_Odivision__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z)). % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2=V_b_2|V_c_2=V_d_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)). % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)). % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_c_2!=V_d_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m). % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_ya_2))|V_w_2=V_xa_2|V_ya_2=V_z_2. % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_ya_2))|V_w_2!=V_xa_2. % 11.02/10.93 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_ya_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_ya_2))|V_ya_2!=V_z_2. % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)). % 11.02/10.93 0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)). % 11.02/10.93 0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)). % 11.02/10.93 0 [] c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)). % 11.02/10.93 0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Ono__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)). % 11.02/10.93 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)). % 11.02/10.93 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)!=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)|V_a_2=V_b_2. % 11.02/10.93 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)|V_a_2!=V_b_2. % 11.02/10.93 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)!=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)|V_a_2=V_b_2. % 11.02/10.93 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)|V_a_2!=V_b_2. % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j)). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)). % 11.02/10.93 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2))|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2))|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 11.02/10.93 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)). % 11.02/10.93 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n)). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2). % 11.02/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 11.02/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 11.02/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 11.02/10.93 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y))). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2)))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x). % 11.02/10.94 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_ea_2),V_c_2),V_d_2). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ea_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_ea_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_ea_2),V_d_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)|c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_b_2). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)). % 11.02/10.94 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)). % 11.02/10.94 0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))). % 11.02/10.94 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_y),V_x)=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 11.02/10.94 0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y). % 11.02/10.94 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))). % 11.02/10.94 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))!=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))!=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_a_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_a_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=c_Int_Onumber__class_Onumber__of(T_a,V_w_2)|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)=V_b_2. % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)!=V_b_2|V_c_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)!=V_b_2|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))=V_b_2. % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))!=V_b_2|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z). % 11.02/10.94 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z). % 11.02/10.94 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)). % 11.02/10.94 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)). % 11.02/10.94 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)). % 11.02/10.94 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)). % 11.02/10.94 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oordered__semiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__ring(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Olinordered__idom(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint). % 11.02/10.94 0 [] class_Divides_Osemiring__div(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oab__group__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oordered__ring(tc_Int_Oint). % 11.02/10.94 0 [] class_Orderings_Opreorder(tc_Int_Oint). % 11.02/10.94 0 [] class_Orderings_Olinorder(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Omonoid__mult(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Omonoid__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Osemiring__1(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Osemiring__0(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ogroup__add(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Omult__zero(tc_Int_Oint). % 11.02/10.94 0 [] class_Orderings_Oorder(tc_Int_Oint). % 11.02/10.94 0 [] class_Int_Oring__char__0(tc_Int_Oint). % 11.02/10.94 0 [] class_Int_Onumber__ring(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Osemiring(tc_Int_Oint). % 11.02/10.94 0 [] class_Orderings_Oord(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oring__1(tc_Int_Oint). % 11.02/10.94 0 [] class_Power_Opower(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Ozero(tc_Int_Oint). % 11.02/10.94 0 [] class_Rings_Oring(tc_Int_Oint). % 11.02/10.94 0 [] class_Int_Onumber(tc_Int_Oint). % 11.02/10.94 0 [] class_Groups_Oone(tc_Int_Oint). % 11.02/10.94 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat). % 11.02/10.94 0 [] class_Divides_Osemiring__div(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat). % 11.02/10.94 0 [] class_Orderings_Opreorder(tc_Nat_Onat). % 11.02/10.94 0 [] class_Orderings_Olinorder(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Omonoid__add(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Osemiring__1(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Osemiring__0(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Omult__zero(tc_Nat_Onat). % 11.02/10.94 0 [] class_Orderings_Oorder(tc_Nat_Onat). % 11.02/10.94 0 [] class_Rings_Osemiring(tc_Nat_Onat). % 11.02/10.94 0 [] class_Orderings_Oord(tc_Nat_Onat). % 11.02/10.94 0 [] class_Power_Opower(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Ozero(tc_Nat_Onat). % 11.02/10.94 0 [] class_Int_Onumber(tc_Nat_Onat). % 11.02/10.94 0 [] class_Groups_Oone(tc_Nat_Onat). % 11.02/10.94 0 [] class_Orderings_Opreorder(tc_HOL_Obool). % 11.02/10.94 0 [] class_Orderings_Oorder(tc_HOL_Obool). % 11.02/10.94 0 [] class_Orderings_Oord(tc_HOL_Obool). % 11.02/10.94 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__field(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Fields_Olinordered__field(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Odivision__ring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Osemiring__1(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Orderings_Oorder(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Int_Oring__char__0(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Int_Onumber__ring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Osemiring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Orderings_Oord(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oring__1(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Fields_Ofield(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Power_Opower(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Ozero(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Rings_Oring(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Int_Onumber(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Groups_Oone(tc_RealDef_Oreal). % 11.02/10.94 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Odivision__ring(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Osemiring__1(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Int_Onumber__ring(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Osemiring(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Oring__1(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Fields_Ofield(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Power_Opower(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Ozero(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Rings_Oring(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Int_Onumber(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Oone(tc_Complex_Ocomplex). % 11.02/10.94 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Ozero__ne_q__one(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Power_Opower(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Int_Onumber(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] class_Groups_Oone(tc_Code__Numeral_Ocode__numeral). % 11.02/10.94 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_s(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),v_n____)),c_Complex_Ocomplex_OComplex(v_x____,v_y____))),v_e____). % 11.02/10.94 end_of_list. % 11.02/10.94 % 11.02/10.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7. % 11.02/10.94 % 11.02/10.94 This ia a non-Horn set with equality. The strategy will be % 11.02/10.94 Knuth-Bendix, ordered hyper_res, factoring, and unit % 11.02/10.94 deletion, with positive clauses in sos and nonpositive % 11.02/10.94 clauses in usable. % 11.02/10.94 % 11.02/10.94 dependent: set(knuth_bendix). % 11.02/10.94 dependent: set(anl_eq). % 11.02/10.94 dependent: set(para_from). % 11.02/10.94 dependent: set(para_into). % 11.02/10.94 dependent: clear(para_from_right). % 11.02/10.94 dependent: clear(para_into_right). % 11.02/10.94 dependent: set(para_from_vars). % 11.02/10.94 dependent: set(eq_units_both_ways). % 11.02/10.94 dependent: set(dynamic_demod_all). % 11.02/10.94 dependent: set(dynamic_demod). % 11.02/10.94 dependent: set(order_eq). % 11.02/10.94 dependent: set(back_demod). % 11.02/10.94 dependent: set(lrpo). % 11.02/10.94 dependent: set(hyper_res). % 11.02/10.94 dependent: set(unit_deletion). % 11.02/10.94 dependent: set(factor). % 11.02/10.94 % 11.02/10.94 ------------> process usable: % 11.02/10.94 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B. % 11.02/10.94 ** KEPT (pick-wt=15): 2 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)). % 11.02/10.94 ** KEPT (pick-wt=19): 3 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E). % 11.02/10.94 ** KEPT (pick-wt=19): 4 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E). % 11.02/10.94 ** KEPT (pick-wt=10): 5 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Ocomplex_OComplex(C,D)|A=C. % 11.02/10.94 ** KEPT (pick-wt=10): 6 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Ocomplex_OComplex(C,D)|B=D. % 11.02/10.94 ** KEPT (pick-wt=13): 7 [] c_Complex_Ocomplex_OComplex(A,B)=c_Complex_Ocomplex_OComplex(C,D)|A!=C|B!=D. % 11.02/10.94 ** KEPT (pick-wt=28): 8 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(G,H,I,A,B),C)=hAPP(c_Fun_Ocomp(J,H,K,D,E),F). % 11.02/10.94 ** KEPT (pick-wt=17): 9 [] c_Fun_Ocomp(A,B,C,D,E)!=F|hAPP(D,hAPP(E,G))=hAPP(F,G). % 11.02/10.94 ** KEPT (pick-wt=24): 10 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)). % 11.02/10.94 Following clause subsumed by 10 during input processing: 0 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)). % 11.02/10.94 ** KEPT (pick-wt=9): 11 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)). % 11.02/10.94 ** KEPT (pick-wt=9): 12 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.94 ** KEPT (pick-wt=10): 13 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=10): 14 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=14): 15 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=14): 16 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=12): 17 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=12): 18 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=13): 19 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=13): 20 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=8): 21 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.94 ** KEPT (pick-wt=19): 22 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,E). % 11.02/10.94 ** KEPT (pick-wt=19): 23 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E). % 11.02/10.94 ** KEPT (pick-wt=12): 24 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C. % 11.02/10.94 ** KEPT (pick-wt=12): 25 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C. % 11.02/10.94 ** KEPT (pick-wt=12): 26 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=12): 27 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=9): 28 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=9): 29 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B. % 11.02/10.94 ** KEPT (pick-wt=13): 30 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=13): 31 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=14): 32 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=14): 33 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=18): 34 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 11.02/10.94 ** KEPT (pick-wt=9): 35 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.94 ** KEPT (pick-wt=17): 36 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E. % 11.02/10.94 ** KEPT (pick-wt=17): 37 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E. % 11.02/10.94 ** KEPT (pick-wt=6): 38 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B). % 11.02/10.94 ** KEPT (pick-wt=8): 39 [] -c_SEQ_Osubse_q(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,hAPP(A,B)). % 11.02/10.94 ** KEPT (pick-wt=11): 40 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B. % 11.02/10.94 ** KEPT (pick-wt=8): 41 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). % 11.02/10.94 ** KEPT (pick-wt=7): 42 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B. % 11.02/10.94 Following clause subsumed by 41 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 11.02/10.94 ** KEPT (pick-wt=7): 43 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B. % 11.02/10.94 Following clause subsumed by 40 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B. % 11.02/10.94 ** KEPT (pick-wt=12): 44 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.94 ** KEPT (pick-wt=12): 45 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.94 ** KEPT (pick-wt=14): 46 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 11.02/10.94 ** KEPT (pick-wt=14): 47 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=14): 48 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 11.02/10.94 ** KEPT (pick-wt=17): 49 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.94 ** KEPT (pick-wt=14): 50 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D. % 11.02/10.94 ** KEPT (pick-wt=14): 51 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D. % 11.02/10.94 ** KEPT (pick-wt=14): 52 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D. % 11.02/10.94 ** KEPT (pick-wt=14): 53 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D. % 11.02/10.94 ** KEPT (pick-wt=11): 54 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.94 ** KEPT (pick-wt=11): 55 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.94 Following clause subsumed by 50 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D. % 11.02/10.94 ** KEPT (pick-wt=14): 56 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D. % 11.02/10.94 Following clause subsumed by 52 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D. % 11.02/10.94 ** KEPT (pick-wt=18): 57 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))). % 11.02/10.94 ** KEPT (pick-wt=26): 58 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,E)). % 11.02/10.94 ** KEPT (pick-wt=9): 59 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B. % 11.02/10.94 ** KEPT (pick-wt=9): 60 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B. % 11.02/10.94 ** KEPT (pick-wt=13): 61 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=13): 62 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=9): 63 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B. % 11.02/10.94 ** KEPT (pick-wt=9): 64 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B. % 11.02/10.94 ** KEPT (pick-wt=16): 65 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D). % 11.02/10.94 ** KEPT (pick-wt=16): 66 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=20): 67 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.94 ** KEPT (pick-wt=16): 68 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)). % 11.02/10.94 ** KEPT (pick-wt=16): 69 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.94 Following clause subsumed by 65 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D). % 11.02/10.94 ** KEPT (pick-wt=16): 70 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D). % 11.02/10.94 Following clause subsumed by 66 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=16): 71 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=16): 72 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=16): 73 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=16): 74 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D). % 11.02/10.94 ** KEPT (pick-wt=16): 75 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D). % 11.02/10.94 ** KEPT (pick-wt=16): 76 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.94 ** KEPT (pick-wt=16): 77 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)). % 11.02/10.94 ** KEPT (pick-wt=20): 78 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.94 Following clause subsumed by 72 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 Following clause subsumed by 74 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D). % 11.02/10.94 ** KEPT (pick-wt=11): 79 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C)=B. % 11.02/10.94 ** KEPT (pick-wt=11): 80 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C)=B. % 11.02/10.94 ** KEPT (pick-wt=11): 81 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.94 ** KEPT (pick-wt=11): 82 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.94 ** KEPT (pick-wt=30): 83 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E)))). % 11.02/10.94 ** KEPT (pick-wt=20): 84 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=18): 85 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,D,B)). % 11.02/10.94 ** KEPT (pick-wt=18): 86 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,B,D)). % 11.02/10.94 ** KEPT (pick-wt=23): 87 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=23): 88 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 ** KEPT (pick-wt=27): 89 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.94 Following clause subsumed by 86 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)). % 11.02/10.94 ** KEPT (pick-wt=15): 90 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=15): 91 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=15): 92 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.94 ** KEPT (pick-wt=15): 93 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.94 ** KEPT (pick-wt=20): 94 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=20): 95 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)). % 11.02/10.94 ** KEPT (pick-wt=15): 96 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=15): 97 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=15): 98 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.94 ** KEPT (pick-wt=15): 99 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.94 ** KEPT (pick-wt=20): 100 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.94 ** KEPT (pick-wt=20): 101 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.94 ** KEPT (pick-wt=18): 102 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C))). % 11.02/10.94 ** KEPT (pick-wt=10): 103 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.94 ** KEPT (pick-wt=10): 104 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.94 ** KEPT (pick-wt=14): 105 [] c_Complex_Ocomplex_OComplex(A,B)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.94 ** KEPT (pick-wt=20): 106 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=20): 107 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=18): 108 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)). % 11.02/10.94 ** KEPT (pick-wt=18): 109 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)). % 11.02/10.94 Following clause subsumed by 108 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)). % 11.02/10.94 Following clause subsumed by 109 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)). % 11.02/10.94 ** KEPT (pick-wt=10): 110 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=16): 111 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 11.02/10.94 ** KEPT (pick-wt=14): 112 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C). % 11.02/10.94 ** KEPT (pick-wt=13): 113 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B. % 11.02/10.94 ** KEPT (pick-wt=14): 114 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 Following clause subsumed by 113 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C. % 11.02/10.94 ** KEPT (pick-wt=13): 115 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C). % 11.02/10.94 ** KEPT (pick-wt=13): 116 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=13): 117 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B). % 11.02/10.94 ** KEPT (pick-wt=13): 118 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D). % 11.02/10.94 Following clause subsumed by 113 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B. % 11.02/10.94 ** KEPT (pick-wt=13): 119 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B. % 11.02/10.94 Following clause subsumed by 111 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 11.02/10.94 ** KEPT (pick-wt=9): 120 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=9): 121 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=9): 122 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 113 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 110 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 111 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)). % 11.02/10.94 ** KEPT (pick-wt=24): 123 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f2(D,C,B,A)),hAPP(D,$f2(D,C,B,A))). % 11.02/10.94 ** KEPT (pick-wt=6): 124 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B). % 11.02/10.94 ** KEPT (pick-wt=13): 125 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=9): 126 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=9): 127 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 125 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C. % 11.02/10.94 ** KEPT (pick-wt=10): 128 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 126 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 11.02/10.94 Following clause subsumed by 125 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 125 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B. % 11.02/10.94 Following clause subsumed by 126 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B. % 11.02/10.94 Following clause subsumed by 125 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=9): 129 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 11.02/10.94 ** KEPT (pick-wt=10): 130 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 130 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 129 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 11.02/10.94 ** KEPT (pick-wt=9): 131 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B. % 11.02/10.94 Following clause subsumed by 130 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=10): 132 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=13): 133 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=13): 134 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B). % 11.02/10.94 ** KEPT (pick-wt=13): 135 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=13): 136 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C). % 11.02/10.94 ** KEPT (pick-wt=14): 137 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=14): 138 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C). % 11.02/10.94 Following clause subsumed by 130 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 125 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=11): 139 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,A)|A=B. % 11.02/10.94 ** KEPT (pick-wt=12): 140 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,C). % 11.02/10.94 ** KEPT (pick-wt=14): 141 [] -c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)). % 11.02/10.94 ** KEPT (pick-wt=12): 142 [] c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f4(A)),hAPP(A,$f3(A))). % 11.02/10.94 ** KEPT (pick-wt=10): 143 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=10): 144 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 144 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=10): 145 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.94 Following clause subsumed by 129 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 11.02/10.94 ** KEPT (pick-wt=13): 146 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C. % 11.02/10.94 ** KEPT (pick-wt=10): 147 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=10): 148 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=14): 149 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 11.02/10.94 Following clause subsumed by 145 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.94 Following clause subsumed by 121 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C. % 11.02/10.94 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B). % 11.02/10.94 Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=13): 150 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C. % 11.02/10.94 ** KEPT (pick-wt=13): 151 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C. % 11.02/10.94 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=13): 152 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 144 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 Following clause subsumed by 147 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.94 Following clause subsumed by 150 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 11.02/10.94 Following clause subsumed by 126 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C. % 11.02/10.94 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C. % 11.02/10.94 Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.94 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.94 ** KEPT (pick-wt=14): 153 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.94 ** KEPT (pick-wt=5): 154 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 11.02/10.94 ** KEPT (pick-wt=16): 155 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 11.02/10.94 ** KEPT (pick-wt=17): 156 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)). % 11.02/10.94 ** KEPT (pick-wt=18): 157 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f5(C,B,A))). % 11.02/10.94 ** KEPT (pick-wt=21): 159 [copy,158,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f5(C,B,A))=B. % 11.02/10.94 ** KEPT (pick-wt=19): 160 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f5(C,B,A))). % 11.02/10.94 Following clause subsumed by 155 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). % 11.02/10.94 Following clause subsumed by 156 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)). % 11.02/10.94 ** KEPT (pick-wt=18): 161 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f6(C,B,A))). % 11.02/10.94 ** KEPT (pick-wt=21): 163 [copy,162,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f6(C,B,A))=B. % 11.02/10.94 ** KEPT (pick-wt=19): 164 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f6(C,B,A))). % 11.02/10.94 ** KEPT (pick-wt=18): 165 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 11.02/10.94 Following clause subsumed by 54 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.94 Following clause subsumed by 55 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B). % 11.02/10.94 ** KEPT (pick-wt=18): 166 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)). % 11.02/10.94 ** KEPT (pick-wt=15): 167 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=15): 168 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.94 ** KEPT (pick-wt=11): 169 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 11.02/10.94 ** KEPT (pick-wt=11): 170 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.94 Following clause subsumed by 169 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 11.02/10.94 ** KEPT (pick-wt=14): 171 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D). % 11.02/10.94 ** KEPT (pick-wt=14): 172 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C). % 11.02/10.94 ** KEPT (pick-wt=20): 173 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C). % 11.02/10.94 ** KEPT (pick-wt=14): 174 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)). % 11.02/10.94 ** KEPT (pick-wt=18): 175 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))). % 11.02/10.94 ** KEPT (pick-wt=13): 176 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B). % 11.02/10.94 ** KEPT (pick-wt=17): 177 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B. % 11.02/10.94 ** KEPT (pick-wt=18): 178 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)). % 11.02/10.94 ** KEPT (pick-wt=11): 179 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B). % 11.02/10.94 ** KEPT (pick-wt=7): 180 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B. % 11.02/10.95 ** KEPT (pick-wt=7): 181 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A. % 11.02/10.95 ** KEPT (pick-wt=4): 182 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A). % 11.02/10.95 Following clause subsumed by 180 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 181 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 11.02/10.95 Following clause subsumed by 182 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A). % 11.02/10.95 ** KEPT (pick-wt=12): 183 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C. % 11.02/10.95 ** KEPT (pick-wt=12): 184 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C. % 11.02/10.95 ** KEPT (pick-wt=12): 185 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C. % 11.02/10.95 ** KEPT (pick-wt=12): 186 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C. % 11.02/10.95 ** KEPT (pick-wt=7): 187 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 ** KEPT (pick-wt=14): 188 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)). % 11.02/10.95 ** KEPT (pick-wt=14): 189 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)). % 11.02/10.95 ** KEPT (pick-wt=13): 190 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A. % 11.02/10.95 ** KEPT (pick-wt=12): 191 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C). % 11.02/10.95 ** KEPT (pick-wt=11): 192 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B. % 11.02/10.95 ** KEPT (pick-wt=20): 193 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C. % 11.02/10.95 ** KEPT (pick-wt=20): 194 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C. % 11.02/10.95 ** KEPT (pick-wt=23): 195 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=22): 196 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.95 Following clause subsumed by 189 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=13): 197 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=13): 198 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=8): 199 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=17): 200 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B). % 11.02/10.95 Following clause subsumed by 154 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 11.02/10.95 ** KEPT (pick-wt=12): 201 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 11.02/10.95 ** KEPT (pick-wt=12): 202 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A). % 11.02/10.95 Following clause subsumed by 199 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.95 Following clause subsumed by 154 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). % 11.02/10.95 ** KEPT (pick-wt=10): 203 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=11): 204 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=11): 205 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=15): 206 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=9): 207 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 Following clause subsumed by 187 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=11): 208 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 ** KEPT (pick-wt=11): 209 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 209 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.95 ** KEPT (pick-wt=11): 210 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C). % 11.02/10.95 ** KEPT (pick-wt=17): 211 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 11.02/10.95 ** KEPT (pick-wt=18): 212 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). % 11.02/10.95 ** KEPT (pick-wt=14): 213 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.95 Following clause subsumed by 55 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.95 Following clause subsumed by 54 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.95 ** KEPT (pick-wt=14): 214 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=14): 215 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=14): 216 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). % 11.02/10.95 ** KEPT (pick-wt=14): 217 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B). % 11.02/10.95 ** KEPT (pick-wt=7): 218 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B). % 11.02/10.95 ** KEPT (pick-wt=7): 219 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A). % 11.02/10.95 Following clause subsumed by 21 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 180 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B. % 11.02/10.95 ** KEPT (pick-wt=11): 220 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B. % 11.02/10.95 Following clause subsumed by 220 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B. % 11.02/10.95 Following clause subsumed by 21 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 187 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B. % 11.02/10.95 Following clause subsumed by 21 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 220 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 11.02/10.95 ** KEPT (pick-wt=18): 221 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)). % 11.02/10.95 ** KEPT (pick-wt=22): 222 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 11.02/10.95 Following clause subsumed by 221 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 11.02/10.95 Following clause subsumed by 21 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 Following clause subsumed by 187 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.95 ** KEPT (pick-wt=12): 224 [copy,223,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f7(B,A))=B. % 11.02/10.95 ** KEPT (pick-wt=10): 225 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C). % 11.02/10.95 ** KEPT (pick-wt=19): 226 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B). % 11.02/10.95 ** KEPT (pick-wt=14): 227 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.95 ** KEPT (pick-wt=14): 228 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.95 ** KEPT (pick-wt=14): 229 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=14): 230 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.95 Following clause subsumed by 82 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.95 Following clause subsumed by 81 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)). % 11.02/10.95 ** KEPT (pick-wt=14): 231 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A)). % 11.02/10.95 ** KEPT (pick-wt=14): 232 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)). % 11.02/10.95 ** KEPT (pick-wt=13): 233 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=B. % 11.02/10.95 ** KEPT (pick-wt=19): 234 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A). % 11.02/10.95 ** KEPT (pick-wt=18): 235 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B). % 11.02/10.95 ** KEPT (pick-wt=18): 236 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B). % 11.02/10.95 ** KEPT (pick-wt=13): 237 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),A)=B. % 11.02/10.95 ** KEPT (pick-wt=16): 238 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=C|B=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A). % 11.02/10.95 ** KEPT (pick-wt=16): 239 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=C|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A). % 11.02/10.95 Following clause subsumed by 234 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A). % 11.02/10.95 ** KEPT (pick-wt=19): 240 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A). % 11.02/10.95 Following clause subsumed by 240 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A). % 11.02/10.95 ** KEPT (pick-wt=18): 241 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)). % 11.02/10.95 Following clause subsumed by 170 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C). % 11.02/10.95 ** KEPT (pick-wt=12): 243 [copy,242,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f8(B,A))=B. % 11.02/10.95 Following clause subsumed by 225 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C). % 11.02/10.95 ** KEPT (pick-wt=17): 244 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D),hAPP(B,C)). % 11.02/10.95 ** KEPT (pick-wt=13): 245 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f10(B,A),$f9(B,A)). % 11.02/10.95 ** KEPT (pick-wt=17): 246 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f9(B,A)),hAPP(B,$f10(B,A))). % 11.02/10.95 ** KEPT (pick-wt=23): 248 [copy,247,flip.2] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E))=c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.95 ** KEPT (pick-wt=9): 249 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B. % 11.02/10.95 ** KEPT (pick-wt=9): 250 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B. % 11.02/10.95 ** KEPT (pick-wt=12): 252 [copy,251,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=B|C=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=12): 254 [copy,253,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)=B|C!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=12): 255 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f11(B,A)). % 11.02/10.95 ** KEPT (pick-wt=15): 256 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f11(B,A)). % 11.02/10.95 ** KEPT (pick-wt=21): 257 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f12(B,A,C))),C). % 11.02/10.95 ** KEPT (pick-wt=11): 258 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B))=c_Groups_Oabs__class_Oabs(A,B). % 11.02/10.95 ** KEPT (pick-wt=8): 259 [] A!=B|c_Complex_ORe(A)=c_Complex_ORe(B). % 11.02/10.95 ** KEPT (pick-wt=8): 260 [] A!=B|c_Complex_OIm(A)=c_Complex_OIm(B). % 11.02/10.95 ** KEPT (pick-wt=13): 261 [] A=B|c_Complex_ORe(A)!=c_Complex_ORe(B)|c_Complex_OIm(A)!=c_Complex_OIm(B). % 11.02/10.95 Following clause subsumed by 261 during input processing: 0 [] c_Complex_ORe(A)!=c_Complex_ORe(B)|c_Complex_OIm(A)!=c_Complex_OIm(B)|A=B. % 11.02/10.95 ** KEPT (pick-wt=12): 262 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=12): 263 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=9): 264 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=12): 265 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.95 ** KEPT (pick-wt=8): 266 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oabs__class_Oabs(A,B)). % 11.02/10.95 ** KEPT (pick-wt=21): 267 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)). % 11.02/10.95 ** KEPT (pick-wt=15): 268 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)). % 11.02/10.95 ** KEPT (pick-wt=11): 269 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B))=c_RealVector_Onorm__class_Onorm(A,B). % 11.02/10.95 ** KEPT (pick-wt=12): 270 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B. % 11.02/10.95 ** KEPT (pick-wt=13): 271 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=13): 272 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=9): 273 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)). % 11.02/10.95 ** KEPT (pick-wt=12): 274 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B. % 11.02/10.95 ** KEPT (pick-wt=13): 275 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=13): 276 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=9): 277 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.95 ** KEPT (pick-wt=18): 278 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))). % 11.02/10.95 ** KEPT (pick-wt=18): 279 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B))). % 11.02/10.95 ** KEPT (pick-wt=18): 280 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 11.02/10.95 ** KEPT (pick-wt=20): 281 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 11.02/10.95 ** KEPT (pick-wt=30): 282 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E)))). % 11.02/10.95 ** KEPT (pick-wt=18): 283 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))). % 11.02/10.95 ** KEPT (pick-wt=23): 284 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)). % 11.02/10.95 ** KEPT (pick-wt=17): 285 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C). % 11.02/10.95 ** KEPT (pick-wt=17): 286 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.95 Following clause subsumed by 286 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.95 ** KEPT (pick-wt=17): 287 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)). % 11.02/10.95 ** KEPT (pick-wt=11): 288 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B). % 11.02/10.95 ** KEPT (pick-wt=20): 289 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))). % 11.02/10.95 ** KEPT (pick-wt=25): 290 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f13(A),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,B)))),v_y____)),A). % 11.02/10.95 ** KEPT (pick-wt=23): 291 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f14(A),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,B))),v_x____)),A). % 11.02/10.95 ** KEPT (pick-wt=18): 292 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B). % 11.02/10.95 ** KEPT (pick-wt=18): 293 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.95 ** KEPT (pick-wt=25): 294 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,C,D)). % 11.02/10.95 ** KEPT (pick-wt=21): 295 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,$f15(C,B,A))),B)|c_SEQ_OBse_q(A,C). % 11.02/10.95 ** KEPT (pick-wt=12): 296 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f16(B,A)). % 11.02/10.95 ** KEPT (pick-wt=15): 297 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f16(B,A)). % 11.02/10.95 ** KEPT (pick-wt=10): 298 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A). % 11.02/10.95 ** KEPT (pick-wt=10): 299 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A). % 11.02/10.95 ** KEPT (pick-wt=9): 300 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.95 ** KEPT (pick-wt=7): 302 [copy,301,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A). % 11.02/10.95 Following clause subsumed by 302 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A). % 11.02/10.95 ** KEPT (pick-wt=9): 303 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A). % 11.02/10.95 ** KEPT (pick-wt=5): 304 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.95 ** KEPT (pick-wt=8): 305 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.95 ** KEPT (pick-wt=8): 306 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)). % 11.02/10.95 ** KEPT (pick-wt=8): 307 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.95 ** KEPT (pick-wt=8): 308 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)). % 11.02/10.95 ** KEPT (pick-wt=10): 309 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))). % 11.02/10.95 ** KEPT (pick-wt=12): 310 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))). % 11.02/10.95 ** KEPT (pick-wt=10): 311 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A). % 11.02/10.95 ** KEPT (pick-wt=32): 312 [] -class_RealVector_Oreal__normed__vector(A)| -class_Orderings_Oord(B)|c_Orderings_Oord__class_Oless__e_q(B,C,$f17(D,C,B,A))| -c_Orderings_Oord__class_Oless__e_q(B,C,E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(D,E)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(D,C)))). % 11.02/10.95 ** KEPT (pick-wt=42): 313 [] -class_RealVector_Oreal__normed__vector(A)| -class_Orderings_Oord(B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(C,D),hAPP(C,$f17(C,D,B,A)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(B,D,E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,E)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(C,D)))). % 11.02/10.95 ** KEPT (pick-wt=16): 314 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f18(C,B,A)). % 11.02/10.95 ** KEPT (pick-wt=24): 315 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),$f18(C,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,D). % 11.02/10.95 ** KEPT (pick-wt=24): 316 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),$f18(C,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,D,C). % 11.02/10.95 ** KEPT (pick-wt=17): 317 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D)). % 11.02/10.95 ** KEPT (pick-wt=13): 318 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(B,A),$f19(B,A)). % 11.02/10.95 ** KEPT (pick-wt=17): 319 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f20(B,A)),hAPP(B,$f19(B,A))). % 11.02/10.95 ** KEPT (pick-wt=13): 320 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,$f21(C,D,B,A))|c_SEQ_OBse_q(A,D). % 11.02/10.95 ** KEPT (pick-wt=17): 321 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f21(C,B,D,A))),C)|c_SEQ_OBse_q(A,B). % 11.02/10.95 ** KEPT (pick-wt=16): 322 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f22(C,B,A)). % 11.02/10.95 ** KEPT (pick-wt=24): 323 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),$f22(C,B,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,D). % 11.02/10.95 ** KEPT (pick-wt=24): 324 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),$f22(C,B,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,D,C). % 11.02/10.95 ** KEPT (pick-wt=24): 325 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N1____,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,A))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.95 ** KEPT (pick-wt=26): 326 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,v_N2____,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,A)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.95 ** KEPT (pick-wt=17): 327 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.95 ** KEPT (pick-wt=16): 328 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B). % 11.02/10.95 ** KEPT (pick-wt=16): 329 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B). % 11.02/10.95 ** KEPT (pick-wt=16): 330 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)). % 11.02/10.95 ** KEPT (pick-wt=16): 331 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)). % 11.02/10.95 ** KEPT (pick-wt=17): 332 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A))=c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls))). % 11.02/10.95 ** KEPT (pick-wt=17): 333 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B))=c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B)). % 11.02/10.95 ** KEPT (pick-wt=14): 334 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))=c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))). % 11.02/10.95 ** KEPT (pick-wt=19): 335 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(B))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)). % 11.02/10.95 ** KEPT (pick-wt=19): 336 [] -class_Fields_Ofield__inverse__zero(A)| -class_RealVector_Oreal__normed__field(A)|c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)). % 11.02/10.95 ** KEPT (pick-wt=9): 337 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(A). % 11.02/10.95 ** KEPT (pick-wt=16): 338 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)). % 11.02/10.95 ** KEPT (pick-wt=16): 339 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Int_OBit1(c_Int_OPls)). % 11.02/10.95 ** KEPT (pick-wt=16): 340 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B). % 11.02/10.95 ** KEPT (pick-wt=16): 341 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),B). % 11.02/10.95 ** KEPT (pick-wt=19): 342 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)). % 11.02/10.95 ** KEPT (pick-wt=15): 343 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,B). % 11.02/10.95 ** KEPT (pick-wt=15): 344 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,B). % 11.02/10.95 ** KEPT (pick-wt=15): 345 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=15): 346 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=21): 347 [] -class_RealVector_Oreal__normed__field(A)|B=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Odivide(A,C,B))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),c_RealVector_Onorm__class_Onorm(A,B)). % 11.02/10.95 ** KEPT (pick-wt=15): 348 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B). % 11.02/10.95 ** KEPT (pick-wt=15): 349 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B). % 11.02/10.95 ** KEPT (pick-wt=15): 350 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=15): 351 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=15): 352 [] -class_Int_Onumber__ring(A)| -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_Int_Onumber__class_Onumber__of(A,B))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,B)). % 11.02/10.95 ** KEPT (pick-wt=8): 354 [copy,353,flip.2] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=9): 355 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 356 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 357 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 358 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=13): 359 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber__ring(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=9): 360 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OPls)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=9): 361 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OPls)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=10): 362 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 363 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 364 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 365 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 362 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 363 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 364 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 365 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 366 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 367 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 366 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 367 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=4): 369 [copy,368,flip.1] c_Int_OBit1(A)!=c_Int_OPls. % 11.02/10.95 ** KEPT (pick-wt=7): 371 [copy,370,flip.1] c_Int_OBit0(A)!=c_Int_OPls|c_Int_OPls=A. % 11.02/10.95 ** KEPT (pick-wt=7): 373 [copy,372,flip.1] c_Int_OBit0(A)=c_Int_OPls|c_Int_OPls!=A. % 11.02/10.95 ** KEPT (pick-wt=13): 374 [] -class_Fields_Ofield(A)| -class_Int_Onumber__ring(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)))=B. % 11.02/10.95 Following clause subsumed by 374 during input processing: 0 [] -class_Fields_Ofield(A)| -class_Int_Onumber__ring(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)))=B. % 11.02/10.95 Following clause subsumed by 369 during input processing: 0 [] c_Int_OBit1(A)!=c_Int_OPls. % 11.02/10.95 ** KEPT (pick-wt=7): 375 [] c_Int_OBit0(A)!=c_Int_OPls|A=c_Int_OPls. % 11.02/10.95 ** KEPT (pick-wt=7): 376 [] c_Int_OBit0(A)=c_Int_OPls|A!=c_Int_OPls. % 11.02/10.95 ** KEPT (pick-wt=12): 377 [] -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)!=C|C=c_Int_Onumber__class_Onumber__of(A,B). % 11.02/10.95 ** KEPT (pick-wt=12): 378 [] -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)=C|C!=c_Int_Onumber__class_Onumber__of(A,B). % 11.02/10.95 ** KEPT (pick-wt=5): 379 [] c_Int_OBit0(A)!=c_Int_OBit1(B). % 11.02/10.95 ** KEPT (pick-wt=5): 380 [] c_Int_OBit1(A)!=c_Int_OBit0(B). % 11.02/10.95 ** KEPT (pick-wt=8): 381 [] c_Int_OBit0(A)!=c_Int_OBit0(B)|A=B. % 11.02/10.95 ** KEPT (pick-wt=8): 382 [] c_Int_OBit0(A)=c_Int_OBit0(B)|A!=B. % 11.02/10.95 ** KEPT (pick-wt=8): 383 [] c_Int_OBit1(A)!=c_Int_OBit1(B)|A=B. % 11.02/10.95 ** KEPT (pick-wt=8): 384 [] c_Int_OBit1(A)=c_Int_OBit1(B)|A!=B. % 11.02/10.95 ** KEPT (pick-wt=14): 385 [] -class_Int_Onumber__ring(A)| -class_Int_Oring__char__0(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Int_Onumber__class_Onumber__of(A,C)|B=C. % 11.02/10.95 ** KEPT (pick-wt=14): 386 [] -class_Int_Onumber__ring(A)| -class_Int_Oring__char__0(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Int_Onumber__class_Onumber__of(A,C)|B!=C. % 11.02/10.95 ** KEPT (pick-wt=10): 387 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls))=B. % 11.02/10.95 ** KEPT (pick-wt=10): 388 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls),B)=B. % 11.02/10.95 ** KEPT (pick-wt=18): 389 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B). % 11.02/10.95 ** KEPT (pick-wt=18): 390 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.95 ** KEPT (pick-wt=21): 391 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.95 ** KEPT (pick-wt=10): 392 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 393 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 392 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 393 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 394 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 395 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 396 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 397 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 394 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 395 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 396 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 397 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 398 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 399 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 400 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=10): 401 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 398 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 399 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 400 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 Following clause subsumed by 401 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.95 ** KEPT (pick-wt=9): 402 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=9): 403 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(A),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=11): 404 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.95 ** KEPT (pick-wt=11): 405 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.95 ** KEPT (pick-wt=9): 406 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=9): 407 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=11): 408 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.95 ** KEPT (pick-wt=11): 409 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.95 ** KEPT (pick-wt=9): 410 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=9): 411 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=21): 412 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.95 Following clause subsumed by 391 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B). % 11.02/10.95 ** KEPT (pick-wt=9): 413 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 414 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 415 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=9): 416 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.95 ** KEPT (pick-wt=5): 417 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.95 ** KEPT (pick-wt=4): 418 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls). % 11.02/10.95 ** KEPT (pick-wt=10): 419 [] -class_RealVector_Oreal__normed__field(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=10): 420 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=10): 421 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.95 ** KEPT (pick-wt=16): 422 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C). % 11.02/10.95 ** KEPT (pick-wt=16): 423 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C). % 11.02/10.95 ** KEPT (pick-wt=16): 424 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). % 11.02/10.95 ** KEPT (pick-wt=16): 425 [] -class_Int_Onumber__ring(A)| -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C). % 11.02/10.95 ** KEPT (pick-wt=20): 426 [] -class_RealVector_Oreal__normed__field(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.95 ** KEPT (pick-wt=20): 427 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.95 ** KEPT (pick-wt=23): 429 [copy,428,flip.2] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)),D)=c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,C),D)). % 11.02/10.95 ** KEPT (pick-wt=17): 431 [copy,430,flip.2] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C))=c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)). % 11.02/10.95 Following clause subsumed by 431 during input processing: 0 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C))=c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)). % 11.02/10.96 ** KEPT (pick-wt=20): 432 [] -class_RealVector_Oreal__normed__field(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=20): 433 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=9): 434 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Oone__class_Oone(A))=B. % 11.02/10.96 ** KEPT (pick-wt=17): 435 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,C))=c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)). % 11.02/10.96 Following clause subsumed by 144 during input processing: 0 [] -class_Int_Onumber(A)| -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)). % 11.02/10.96 Following clause subsumed by 143 during input processing: 0 [] -class_Int_Onumber(A)| -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B)). % 11.02/10.96 ** KEPT (pick-wt=13): 436 [] -class_Rings_Odivision__ring__inverse__zero(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,B,B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.96 ** KEPT (pick-wt=13): 437 [] -class_Rings_Odivision__ring__inverse__zero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,B,B)=c_Groups_Oone__class_Oone(A). % 11.02/10.96 ** KEPT (pick-wt=13): 438 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,B,B)=c_Groups_Oone__class_Oone(A). % 11.02/10.96 ** KEPT (pick-wt=16): 439 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,C,B)!=c_Groups_Oone__class_Oone(A)|C=B. % 11.02/10.96 ** KEPT (pick-wt=16): 440 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,C,B)=c_Groups_Oone__class_Oone(A)|C!=B. % 11.02/10.96 ** KEPT (pick-wt=23): 441 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,C),D))=c_Groups_Ominus__class_Ominus(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)),D). % 11.02/10.96 ** KEPT (pick-wt=18): 442 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B). % 11.02/10.96 ** KEPT (pick-wt=18): 443 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=18): 444 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.96 ** KEPT (pick-wt=18): 445 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=18): 446 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.96 ** KEPT (pick-wt=18): 447 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=10): 448 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=10): 449 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=14): 450 [] c_Complex_Ocomplex_OComplex(A,B)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=26): 451 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c1,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,A)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.96 ** KEPT (pick-wt=24): 452 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c2,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,A))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.96 ** KEPT (pick-wt=9): 453 [] -class_Int_Onumber__ring(A)|c_Groups_Oone__class_Oone(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)). % 11.02/10.96 ** KEPT (pick-wt=20): 455 [copy,454,flip.3] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),B). % 11.02/10.96 ** KEPT (pick-wt=21): 456 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A)))). % 11.02/10.96 ** KEPT (pick-wt=11): 457 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=10): 458 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). % 11.02/10.96 ** KEPT (pick-wt=10): 459 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). % 11.02/10.96 ** KEPT (pick-wt=12): 460 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 461 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 462 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 463 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=15): 464 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A=B. % 11.02/10.96 ** KEPT (pick-wt=12): 465 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=11): 466 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|A!=B. % 11.02/10.96 ** KEPT (pick-wt=11): 467 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=11): 468 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=12): 469 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 470 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=17): 471 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=17): 472 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=14): 473 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)). % 11.02/10.96 Following clause subsumed by 470 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B). % 11.02/10.96 ** KEPT (pick-wt=5): 474 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=12): 475 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 476 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 477 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 478 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 479 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=12): 480 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=8): 481 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=7): 482 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A!=B. % 11.02/10.96 ** KEPT (pick-wt=11): 483 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|A=B. % 11.02/10.96 ** KEPT (pick-wt=14): 484 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)). % 11.02/10.96 ** KEPT (pick-wt=14): 485 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)). % 11.02/10.96 ** KEPT (pick-wt=18): 486 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C,D)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)). % 11.02/10.96 ** KEPT (pick-wt=11): 487 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,A)|A=B. % 11.02/10.96 ** KEPT (pick-wt=12): 488 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,C). % 11.02/10.96 ** KEPT (pick-wt=10): 489 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=10): 490 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=10): 491 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=10): 492 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=16): 493 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B). % 11.02/10.96 ** KEPT (pick-wt=12): 494 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=16): 495 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=16): 496 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B). % 11.02/10.96 ** KEPT (pick-wt=20): 497 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A). % 11.02/10.96 ** KEPT (pick-wt=16): 498 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=12): 499 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 500 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=11): 501 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.96 ** KEPT (pick-wt=11): 502 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,A). % 11.02/10.96 ** KEPT (pick-wt=12): 503 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,C)|A=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C). % 11.02/10.96 ** KEPT (pick-wt=11): 504 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,C)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=16): 505 [] c_Complex_Ocomplex_OComplex(A,B)=c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,C)|A!=c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,C)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=17): 506 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)). % 11.02/10.96 ** KEPT (pick-wt=20): 507 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 508 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 509 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 510 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 511 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 512 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 513 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 514 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 515 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 516 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 517 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 518 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=21): 519 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=21): 520 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)). % 11.02/10.96 ** KEPT (pick-wt=20): 521 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 522 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 523 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 524 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 525 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 526 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 527 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 528 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 529 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 530 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 531 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 532 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C). % 11.02/10.96 ** KEPT (pick-wt=20): 533 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)). % 11.02/10.96 ** KEPT (pick-wt=20): 534 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 535 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 536 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)). % 11.02/10.96 ** KEPT (pick-wt=21): 537 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=21): 538 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)). % 11.02/10.96 Following clause subsumed by 354 during input processing: 0 [] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OPls). % 11.02/10.96 ** KEPT (pick-wt=21): 539 [] -class_Fields_Olinordered__field(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)). % 11.02/10.96 ** KEPT (pick-wt=20): 540 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)). % 11.02/10.96 ** KEPT (pick-wt=20): 541 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=30): 542 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=30): 543 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=30): 544 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)). % 11.02/10.96 ** KEPT (pick-wt=20): 545 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.96 ** KEPT (pick-wt=20): 546 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)). % 11.02/10.96 ** KEPT (pick-wt=21): 547 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))),C). % 11.02/10.96 ** KEPT (pick-wt=21): 548 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=15): 549 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A))). % 11.02/10.96 ** KEPT (pick-wt=15): 550 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A))). % 11.02/10.96 ** KEPT (pick-wt=18): 551 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)). % 11.02/10.96 ** KEPT (pick-wt=24): 552 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c3,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,A))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.96 ** KEPT (pick-wt=26): 553 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$c4,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,A)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.96 ** KEPT (pick-wt=48): 554 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=18): 555 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 11.02/10.96 ** KEPT (pick-wt=14): 556 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=4): 558 [copy,557,flip.1] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)!=c_Complex_Oii. % 11.02/10.96 ** KEPT (pick-wt=4): 560 [copy,559,flip.1] c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)!=c_Complex_Oii. % 11.02/10.96 ** KEPT (pick-wt=5): 562 [copy,561,flip.1] c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,A)!=c_Complex_Oii. % 11.02/10.96 ** KEPT (pick-wt=10): 563 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_RComplete_Onatceiling(B)). % 11.02/10.96 ** KEPT (pick-wt=10): 564 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=9): 565 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Oii|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=9): 566 [] c_Complex_Ocomplex_OComplex(A,B)!=c_Complex_Oii|B=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=13): 567 [] c_Complex_Ocomplex_OComplex(A,B)=c_Complex_Oii|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=14): 568 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_Osucc(B))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)). % 11.02/10.96 ** KEPT (pick-wt=11): 569 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=11): 570 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=14): 571 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))=c_Groups_Oone__class_Oone(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=24): 572 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)). % 11.02/10.96 ** KEPT (pick-wt=22): 573 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). % 11.02/10.96 ** KEPT (pick-wt=22): 574 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)). % 11.02/10.96 ** KEPT (pick-wt=14): 575 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Int_OPls)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=3): 576 [] -c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=3): 577 [] -c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=11): 578 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(A)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=11): 579 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(A)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=7): 580 [] -c_Nat__Numeral_Oneg(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A). % 11.02/10.96 ** KEPT (pick-wt=7): 581 [] -c_Nat__Numeral_Oneg(A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=7): 582 [] c_Nat__Numeral_Oneg(A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=9): 583 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A)))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.96 ** KEPT (pick-wt=9): 584 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(A)))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.96 ** KEPT (pick-wt=4): 585 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)). % 11.02/10.96 ** KEPT (pick-wt=9): 586 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A)))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.96 ** KEPT (pick-wt=9): 587 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A)))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.96 ** KEPT (pick-wt=9): 588 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(A),B). % 11.02/10.96 ** KEPT (pick-wt=9): 589 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(A),B). % 11.02/10.96 ** KEPT (pick-wt=10): 590 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=18): 591 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.96 ** KEPT (pick-wt=21): 592 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.96 ** KEPT (pick-wt=18): 593 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)!=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|A=B. % 11.02/10.96 ** KEPT (pick-wt=18): 594 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|A!=B. % 11.02/10.96 ** KEPT (pick-wt=21): 595 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)). % 11.02/10.96 ** KEPT (pick-wt=20): 596 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A!=B. % 11.02/10.96 ** KEPT (pick-wt=18): 597 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.96 ** KEPT (pick-wt=21): 598 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|A!=B. % 11.02/10.96 ** KEPT (pick-wt=24): 599 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B)). % 11.02/10.96 ** KEPT (pick-wt=23): 600 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A!=B. % 11.02/10.96 ** KEPT (pick-wt=22): 601 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),C))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),C). % 11.02/10.96 ** KEPT (pick-wt=26): 602 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B),C))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),C). % 11.02/10.96 ** KEPT (pick-wt=24): 603 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)). % 11.02/10.96 ** KEPT (pick-wt=22): 604 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_RComplete_Onatfloor(B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B). % 11.02/10.96 ** KEPT (pick-wt=22): 605 [] c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_RComplete_Onatfloor(B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,A),B). % 11.02/10.96 ** KEPT (pick-wt=18): 606 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 11.02/10.96 ** KEPT (pick-wt=10): 607 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_RComplete_Onatfloor(B)). % 11.02/10.96 ** KEPT (pick-wt=10): 608 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=11): 609 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.96 ** KEPT (pick-wt=11): 610 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.96 ** KEPT (pick-wt=12): 611 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Nat__Transfer_Otsub(B,A)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A). % 11.02/10.96 ** KEPT (pick-wt=24): 612 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)). % 11.02/10.96 ** KEPT (pick-wt=10): 613 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_RealDef_Oreal(tc_Nat_Onat,B)|A=B. % 11.02/10.96 ** KEPT (pick-wt=10): 614 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_RealDef_Oreal(tc_Nat_Onat,B)|A!=B. % 11.02/10.96 ** KEPT (pick-wt=10): 615 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=10): 616 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=7): 617 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.96 ** KEPT (pick-wt=12): 618 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 619 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 620 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.96 ** KEPT (pick-wt=12): 621 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B). % 11.02/10.96 ** KEPT (pick-wt=11): 622 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=11): 623 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=19): 624 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),c_RealDef_Oreal(tc_Nat_Onat,A)). % 11.02/10.96 ** KEPT (pick-wt=12): 625 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A)),A). % 11.02/10.96 ** KEPT (pick-wt=11): 626 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_RComplete_Onatfloor(B)). % 11.02/10.96 ** KEPT (pick-wt=11): 627 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B). % 11.02/10.96 ** KEPT (pick-wt=12): 628 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.96 ** KEPT (pick-wt=12): 629 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.96 ** KEPT (pick-wt=16): 630 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,B)). % 11.02/10.96 ** KEPT (pick-wt=16): 631 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,B)). % 11.02/10.96 ** KEPT (pick-wt=16): 632 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 11.02/10.96 ** KEPT (pick-wt=16): 633 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))). % 11.02/10.96 ** KEPT (pick-wt=16): 634 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A). % 11.02/10.96 Following clause subsumed by 626 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A). % 11.02/10.96 ** KEPT (pick-wt=16): 635 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 11.02/10.96 Following clause subsumed by 627 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 11.02/10.96 ** KEPT (pick-wt=19): 636 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_RealDef_Oreal(tc_Nat_Onat,A)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(B),A). % 11.02/10.96 ** KEPT (pick-wt=19): 637 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_RealDef_Oreal(tc_Nat_Onat,A)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(B),A). % 11.02/10.96 ** KEPT (pick-wt=17): 638 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(A,B)). % 11.02/10.96 ** KEPT (pick-wt=16): 639 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(A),B). % 11.02/10.96 ** KEPT (pick-wt=12): 640 [] -c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_RealDef_Oreal(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.96 ** KEPT (pick-wt=18): 641 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),B). % 11.02/10.96 Following clause subsumed by 611 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|c_Nat__Transfer_Otsub(B,A)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A). % 11.02/10.96 ** KEPT (pick-wt=15): 642 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)). % 11.02/10.96 ** KEPT (pick-wt=20): 643 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(B)=A. % 11.02/10.96 ** KEPT (pick-wt=18): 644 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(A),B). % 11.02/10.96 ** KEPT (pick-wt=16): 645 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f23(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))),A). % 11.02/10.96 ** KEPT (pick-wt=12): 646 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,$f23(A))). % 11.02/10.96 ** KEPT (pick-wt=23): 647 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(A),B). % 11.02/10.96 ** KEPT (pick-wt=32): 648 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.96 ** KEPT (pick-wt=28): 649 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.96 ** KEPT (pick-wt=28): 650 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|C=c_Groups_Ozero__class_Ozero(A). % 11.02/10.96 ** KEPT (pick-wt=17): 652 [copy,651,flip.1] c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A))!=A|c_RComplete_Onatfloor(c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,B))=c_Power_Opower__class_Opower(tc_Nat_Onat,c_RComplete_Onatfloor(A),B). % 11.02/10.96 ** KEPT (pick-wt=9): 653 [] -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,B,c_Groups_Oone__class_Oone(tc_Nat_Onat))=B. % 11.02/10.96 ** KEPT (pick-wt=15): 654 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,c_Power_Opower__class_Opower(A,B,C))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C). % 11.02/10.96 ** KEPT (pick-wt=16): 655 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)). % 11.02/10.96 ** KEPT (pick-wt=10): 656 [] -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A). % 11.02/10.96 ** KEPT (pick-wt=17): 657 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.96 ** KEPT (pick-wt=12): 658 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.96 ** KEPT (pick-wt=13): 659 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.96 ** KEPT (pick-wt=13): 660 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,A,B)). % 11.02/10.97 ** KEPT (pick-wt=21): 661 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=23): 662 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=27): 663 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 Following clause subsumed by 657 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.97 Following clause subsumed by 658 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 Following clause subsumed by 659 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.97 ** KEPT (pick-wt=20): 664 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=20): 665 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=18): 666 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=14): 667 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=17): 668 [] -class_Rings_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=17): 669 [] -class_Rings_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=14): 670 [] -class_Rings_Osemiring__1(A)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=14): 671 [] -class_Rings_Osemiring__1(A)|c_Power_Opower__class_Opower(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=21): 672 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 11.02/10.97 ** KEPT (pick-wt=21): 673 [] -class_Rings_Olinordered__idom(A)|c_Power_Opower__class_Opower(A,c_Groups_Oabs__class_Oabs(A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). % 11.02/10.97 ** KEPT (pick-wt=32): 674 [] -class_Rings_Olinordered__semidom(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|B=C. % 11.02/10.97 ** KEPT (pick-wt=29): 675 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C). % 11.02/10.97 ** KEPT (pick-wt=14): 676 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.97 ** KEPT (pick-wt=14): 677 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.97 ** KEPT (pick-wt=18): 678 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|B!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=18): 679 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=27): 680 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=27): 681 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=31): 682 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=25): 683 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=25): 684 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=29): 685 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=29): 686 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,C). % 11.02/10.97 ** KEPT (pick-wt=24): 687 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). % 11.02/10.97 ** KEPT (pick-wt=28): 688 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=28): 689 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A))|C=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=32): 690 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=24): 691 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A)). % 11.02/10.97 ** KEPT (pick-wt=21): 692 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.97 ** KEPT (pick-wt=17): 693 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.97 ** KEPT (pick-wt=19): 694 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=10): 695 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=10): 696 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=9): 697 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(A,B,c_Groups_Oone__class_Oone(A))=B. % 11.02/10.97 ** KEPT (pick-wt=14): 698 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C)). % 11.02/10.97 ** KEPT (pick-wt=13): 699 [] -class_Divides_Osemiring__div(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Divides_Odiv__class_Odiv(A,B,B)=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=11): 700 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=22): 702 [copy,701,flip.3] -class_Divides_Osemiring__div(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Groups_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,C,B),B). % 11.02/10.97 ** KEPT (pick-wt=22): 704 [copy,703,flip.3] -class_Divides_Osemiring__div(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Groups_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,B,C),B). % 11.02/10.97 ** KEPT (pick-wt=19): 705 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,B),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A)). % 11.02/10.97 ** KEPT (pick-wt=17): 706 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),B). % 11.02/10.97 ** KEPT (pick-wt=26): 707 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D)|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,C,D)). % 11.02/10.97 ** KEPT (pick-wt=28): 709 [copy,708,flip.4] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Rings_Oinverse__class_Odivide(A,c_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,B,C))=c_Power_Opower__class_Opower(A,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,D,C)). % 11.02/10.97 ** KEPT (pick-wt=20): 710 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C)). % 11.02/10.97 ** KEPT (pick-wt=18): 711 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)). % 11.02/10.97 ** KEPT (pick-wt=18): 712 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=18): 713 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 ** KEPT (pick-wt=18): 714 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 ** KEPT (pick-wt=18): 715 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 Following clause subsumed by 712 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=21): 716 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=20): 717 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). % 11.02/10.97 ** KEPT (pick-wt=20): 718 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=19): 719 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). % 11.02/10.97 ** KEPT (pick-wt=11): 720 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B!=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.97 ** KEPT (pick-wt=16): 721 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B). % 11.02/10.97 ** KEPT (pick-wt=16): 722 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A). % 11.02/10.97 ** KEPT (pick-wt=18): 723 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 ** KEPT (pick-wt=18): 724 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 ** KEPT (pick-wt=17): 725 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.97 ** KEPT (pick-wt=17): 726 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B). % 11.02/10.97 ** KEPT (pick-wt=17): 727 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,A). % 11.02/10.97 ** KEPT (pick-wt=18): 728 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 Following clause subsumed by 726 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B). % 11.02/10.97 ** KEPT (pick-wt=24): 729 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)). % 11.02/10.97 ** KEPT (pick-wt=18): 730 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 Following clause subsumed by 721 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.97 ** KEPT (pick-wt=18): 731 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=18): 732 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=18): 733 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). % 11.02/10.97 ** KEPT (pick-wt=24): 734 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,C)). % 11.02/10.97 Following clause subsumed by 722 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint). % 11.02/10.97 ** KEPT (pick-wt=19): 735 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C)). % 11.02/10.97 ** KEPT (pick-wt=19): 736 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,C)). % 11.02/10.97 ** KEPT (pick-wt=17): 737 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B),A). % 11.02/10.97 ** KEPT (pick-wt=26): 738 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(B)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(A)))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,B),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,A)). % 11.02/10.97 ** KEPT (pick-wt=13): 739 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Power_Opower__class_Opower(A,B,C)!=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=10): 740 [] -class_Groups_Omonoid__mult(A)|c_Power_Opower__class_Opower(A,c_Groups_Oone__class_Oone(A),B)=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=20): 742 [copy,741,flip.2] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,D,C))=c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,B,D),C). % 11.02/10.97 ** KEPT (pick-wt=15): 743 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Power_Opower__class_Opower(A,B,C))=c_Power_Opower__class_Opower(A,c_Groups_Oabs__class_Oabs(A,B),C). % 11.02/10.97 ** KEPT (pick-wt=9): 744 [] -class_Groups_Omonoid__mult(A)|c_Power_Opower__class_Opower(A,B,c_Groups_Oone__class_Oone(tc_Nat_Onat))=B. % 11.02/10.97 ** KEPT (pick-wt=21): 745 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,D),c_Power_Opower__class_Opower(A,C,D)). % 11.02/10.97 ** KEPT (pick-wt=15): 746 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C)). % 11.02/10.97 ** KEPT (pick-wt=15): 747 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C)). % 11.02/10.97 ** KEPT (pick-wt=15): 748 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C)). % 11.02/10.97 ** KEPT (pick-wt=19): 749 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=19): 750 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=23): 751 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|c_Power_Opower__class_Opower(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=19): 752 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Power_Opower__class_Opower(A,B,C)!=c_Power_Opower__class_Opower(A,B,D)|C=D. % 11.02/10.97 ** KEPT (pick-wt=19): 753 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Power_Opower__class_Opower(A,B,C)=c_Power_Opower__class_Opower(A,B,D)|C!=D. % 11.02/10.97 ** KEPT (pick-wt=24): 755 [copy,754,flip.3] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Power_Opower__class_Opower(A,C,D),c_Power_Opower__class_Opower(A,B,D))=c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,C,B),D). % 11.02/10.97 ** KEPT (pick-wt=10): 756 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=19): 757 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Power_Opower__class_Opower(A,B,C))=c_Power_Opower__class_Opower(A,c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B),C). % 11.02/10.97 Following clause subsumed by 657 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 Following clause subsumed by 659 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A). % 11.02/10.97 Following clause subsumed by 658 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat). % 11.02/10.97 ** KEPT (pick-wt=19): 758 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,A,B),c_Power_Opower__class_Opower(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C). % 11.02/10.97 ** KEPT (pick-wt=21): 759 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,B,D). % 11.02/10.97 ** KEPT (pick-wt=16): 760 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Oone__class_Oone(A). % 11.02/10.97 ** KEPT (pick-wt=16): 761 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A). % 11.02/10.97 ** KEPT (pick-wt=12): 762 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,c_Groups_Oabs__class_Oabs(A,B),C)). % 11.02/10.97 ** KEPT (pick-wt=21): 763 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D)|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,D,B),c_Power_Opower__class_Opower(A,D,C)). % 11.02/10.97 ** KEPT (pick-wt=21): 764 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 11.02/10.97 Following clause subsumed by 764 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 11.02/10.97 Following clause subsumed by 763 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D). % 11.02/10.97 ** KEPT (pick-wt=21): 765 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,D,B),c_Power_Opower__class_Opower(A,D,C)). % 11.02/10.97 ** KEPT (pick-wt=26): 766 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,D,C),c_Power_Opower__class_Opower(A,D,B)). % 11.02/10.97 ** KEPT (pick-wt=29): 767 [] -class_Rings_Olinordered__semidom(A)|c_Power_Opower__class_Opower(A,B,C)!=c_Power_Opower__class_Opower(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|B=D. % 11.02/10.97 ** KEPT (pick-wt=26): 768 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,D,C),c_Power_Opower__class_Opower(A,D,B)). % 11.02/10.97 ** KEPT (pick-wt=21): 769 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 11.02/10.97 ** KEPT (pick-wt=21): 770 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 11.02/10.97 Following clause subsumed by 769 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D). % 11.02/10.97 ** KEPT (pick-wt=59): 771 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),A). % 11.02/10.97 ** KEPT (pick-wt=9): 772 [] c_NthRoot_Osqrt(A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=9): 773 [] c_NthRoot_Osqrt(A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 Following clause subsumed by 772 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_NthRoot_Osqrt(A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=11): 774 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A)). % 11.02/10.97 ** KEPT (pick-wt=11): 775 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 776 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 777 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 Following clause subsumed by 774 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 778 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A)). % 11.02/10.97 ** KEPT (pick-wt=10): 779 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_NthRoot_Osqrt(A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=11): 780 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 781 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 782 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 Following clause subsumed by 778 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 783 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 784 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 785 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 786 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.97 Following clause subsumed by 784 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A)). % 11.02/10.97 ** KEPT (pick-wt=11): 787 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 788 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=11): 789 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=11): 790 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)). % 11.02/10.97 ** KEPT (pick-wt=8): 791 [] c_NthRoot_Osqrt(A)!=c_NthRoot_Osqrt(B)|A=B. % 11.02/10.97 ** KEPT (pick-wt=8): 792 [] c_NthRoot_Osqrt(A)=c_NthRoot_Osqrt(B)|A!=B. % 11.02/10.97 ** KEPT (pick-wt=10): 793 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 11.02/10.97 ** KEPT (pick-wt=10): 794 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B). % 11.02/10.97 Following clause subsumed by 794 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B)). % 11.02/10.97 ** KEPT (pick-wt=10): 795 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). % 11.02/10.97 ** KEPT (pick-wt=10): 796 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B). % 11.02/10.97 Following clause subsumed by 796 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_NthRoot_Osqrt(B)). % 11.02/10.97 ** KEPT (pick-wt=9): 797 [] c_NthRoot_Osqrt(A)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=9): 798 [] c_NthRoot_Osqrt(A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=16): 799 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=A|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 ** KEPT (pick-wt=16): 800 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=A| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A). % 11.02/10.97 Following cla % 11.02/10.97 Search stopped in tp_alloc by max_mem option. % 11.02/10.97 use subsumed by 800 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=A. % 11.02/10.97 ** KEPT (pick-wt=19): 801 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=B| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_NthRoot_Osqrt(B)=A. % 11.02/10.97 ** KEPT (pick-wt=18): 802 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). % 11.02/10.97 ** KEPT (pick-wt=17): 803 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),A). % 11.02/10.97 ** KEPT (pick-wt=25): 804 [] c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))!=B|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=25): 805 [] c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))!=A|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). % 11.02/10.97 ** KEPT (pick-wt=50): 806 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),B). % 11.02/10.97 % 11.02/10.97 Search stopped in tp_alloc by max_mem option. % 11.02/10.97 % 11.02/10.97 ============ end of search ============ % 11.02/10.97 % 11.02/10.97 -------------- statistics ------------- % 11.02/10.97 clauses given 0 % 11.02/10.97 clauses generated 0 % 11.02/10.97 clauses kept 782 % 11.02/10.97 clauses forward subsumed 128 % 11.02/10.97 clauses back subsumed 0 % 11.02/10.97 Kbytes malloced 11718 % 11.02/10.97 % 11.02/10.97 ----------- times (seconds) ----------- % 11.02/10.97 user CPU time 0.18 (0 hr, 0 min, 0 sec) % 11.02/10.97 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 11.02/10.97 wall-clock time 11 (0 hr, 0 min, 11 sec) % 11.02/10.97 % 11.02/10.97 Process 31033 finished Wed Jul 27 02:53:51 2022 % 11.02/10.97 Otter interrupted % 11.02/10.97 PROOF NOT FOUND %------------------------------------------------------------------------------