TSTP Solution File: SWW216+1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW216+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 13:22:10 EDT 2022

% Result   : Unknown 12.41s 12.31s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWW216+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n012.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 03:04:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 12.26/12.23  ----- Otter 3.3f, August 2004 -----
% 12.26/12.23  The process was started by sandbox on n012.cluster.edu,
% 12.26/12.23  Wed Jul 27 03:04:50 2022
% 12.26/12.23  The command was "./otter".  The process ID is 11308.
% 12.26/12.23  
% 12.26/12.23  set(prolog_style_variables).
% 12.26/12.23  set(auto).
% 12.26/12.23     dependent: set(auto1).
% 12.26/12.23     dependent: set(process_input).
% 12.26/12.23     dependent: clear(print_kept).
% 12.26/12.23     dependent: clear(print_new_demod).
% 12.26/12.23     dependent: clear(print_back_demod).
% 12.26/12.23     dependent: clear(print_back_sub).
% 12.26/12.23     dependent: set(control_memory).
% 12.26/12.23     dependent: assign(max_mem, 12000).
% 12.26/12.23     dependent: assign(pick_given_ratio, 4).
% 12.26/12.23     dependent: assign(stats_level, 1).
% 12.26/12.23     dependent: assign(max_seconds, 10800).
% 12.26/12.23  clear(print_given).
% 12.26/12.23  
% 12.26/12.23  formula_list(usable).
% 12.26/12.23  all A (A=A).
% 12.26/12.23  all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)).
% 12.26/12.23  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,v_m____)).
% 12.26/12.23  all V_w V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z)).
% 12.26/12.23  all V_z3 V_z2 V_z1 (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3))).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____).
% 12.26/12.23  all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)=V_a).
% 12.26/12.23  all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x)=V_x).
% 12.26/12.23  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a)).
% 12.26/12.23  all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.23  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ry))).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.23  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.23  c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.23  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 12.26/12.23  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 12.26/12.23  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 (V_ca_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_b_2)<->V_a_2=V_b_2)).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 (V_ca_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2),V_ca_2)<->V_a_2=V_b_2)).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_y)))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)))).
% 12.26/12.23  all V_y_2 V_x_2 V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 12.26/12.23  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_ry))).
% 12.26/12.23  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_ry))).
% 12.26/12.23  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)))).
% 12.26/12.23  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx)=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ly)).
% 12.26/12.23  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_rx))).
% 12.26/12.23  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ry)).
% 12.26/12.23  -(all B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))))).
% 12.26/12.23  exists B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))).
% 12.26/12.23  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),hAPP(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)))))).
% 12.26/12.23  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),hAPP(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)))))).
% 12.26/12.23  all V_a_2 V_b_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))))).
% 12.26/12.23  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,hAPP(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))))).
% 12.26/12.23  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,hAPP(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)))).
% 12.26/12.23  all V_a_2 V_b_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)))).
% 12.26/12.23  all V_a_2 V_ca_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_ca_2),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_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))))).
% 12.26/12.23  all V_ca_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_ca_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_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)))))).
% 12.26/12.23  all V_w V_z V_y V_x T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))).
% 12.26/12.23  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)))).
% 12.26/12.23  all V_wa_2 V_x_2 V_za_2 V_y_2 T_a (class_Fields_Ofield(T_a)-> (V_y_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_za_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)<->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 12.26/12.23  all V_a_2 V_ca_2 V_b_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))& (V_ca_2=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.23  all V_ca_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_ca_2)<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)=V_b_2)& (V_ca_2=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.23  all V_x_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.23  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))).
% 12.26/12.23  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))).
% 12.26/12.23  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))).
% 12.26/12.23  all V_b V_a V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (hAPP(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)))).
% 12.26/12.23  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=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c)->c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a))).
% 12.26/12.23  all V_a_2 V_b_2 V_ca_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2<->V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)<->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)=V_b_2))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_m),V_n))))).
% 12.26/12.23  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))).
% 12.26/12.23  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))).
% 12.26/12.23  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)))).
% 12.26/12.23  all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(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))).
% 12.26/12.23  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)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.23  all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(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))).
% 12.26/12.23  all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  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)).
% 12.26/12.23  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)).
% 12.26/12.23  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)).
% 12.26/12.23  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)).
% 12.26/12.23  all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c)).
% 12.26/12.23  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).
% 12.26/12.23  all V_a V_r (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r)).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))).
% 12.26/12.23  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),hAPP(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)))).
% 12.26/12.23  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),hAPP(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)))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_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_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))).
% 12.26/12.23  all V_b_2 V_ca_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))).
% 12.26/12.23  all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.23  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____).
% 12.26/12.23  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)).
% 12.26/12.23  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 12.26/12.23  all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 12.26/12.23  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 12.26/12.23  all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 12.26/12.23  all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.23  all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.26/12.23  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)).
% 12.26/12.23  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))).
% 12.26/12.23  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)).
% 12.26/12.23  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)&V_x_2!=V_y_2).
% 12.26/12.23  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))))).
% 12.26/12.23  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,hAPP(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))).
% 12.26/12.23  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),hAPP(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)))).
% 12.26/12.23  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a))).
% 12.26/12.23  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))).
% 12.26/12.23  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))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))))).
% 12.26/12.23  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))).
% 12.26/12.23  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)))).
% 12.26/12.23  all V_y_2 V_x_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_x_2,V_y_2))<-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_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_y_2))& (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_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_ca_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)))).
% 12.26/12.23  all V_b_2 V_a_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.23  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d))))))).
% 12.26/12.24  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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)))).
% 12.26/12.24  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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)))).
% 12.26/12.24  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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)))).
% 12.26/12.24  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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)))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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)))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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)))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x),V_x))))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_x))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))))).
% 12.26/12.24  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))))))).
% 12.26/12.24  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))))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_y_2 V_x_2 V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 12.26/12.24  all V_y_2 V_x_2 V_za_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 12.26/12.24  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))).
% 12.26/12.24  all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_ca_2 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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_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)))))).
% 12.26/12.24  all V_a_2 V_ca_2 V_b_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_b_2,V_ca_2),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_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))))).
% 12.26/12.24  all V_b_2 V_a_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)))).
% 12.26/12.24  all V_a_2 V_b_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))))).
% 12.26/12.24  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__e_q(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)))).
% 12.26/12.24  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__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 12.26/12.24  all V_b_2 V_a_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))))).
% 12.26/12.24  all V_a_2 V_b_2 V_ca_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,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_2,V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)))).
% 12.26/12.24  all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,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_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 12.26/12.24  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(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 12.26/12.24  all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 12.26/12.24  all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 12.26/12.24  all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 12.26/12.24  all V_y V_x T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> ((all B_z (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)-> (c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,B_z),V_x),V_y))))->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 12.26/12.24  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a))))))).
% 12.26/12.24  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a))))))).
% 12.26/12.24  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 12.26/12.24  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(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_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.26/12.24  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a).
% 12.26/12.24  all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a)).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)<->V_a_2=V_b_2)).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)->V_a=V_b)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_ca_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_ca_2)<->V_b_2=V_ca_2)).
% 12.26/12.24  all V_ca_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_ca_2,V_a_2)<->V_b_2=V_ca_2)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 12.26/12.24  all T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->V_a=V_b)))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a)).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 12.26/12.24  all V_x_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a)).
% 12.26/12.24  c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.24  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).
% 12.26/12.24  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).
% 12.26/12.24  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))).
% 12.26/12.24  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).
% 12.26/12.24  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).
% 12.26/12.24  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))).
% 12.26/12.24  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).
% 12.26/12.24  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).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_b_2 V_a_2 V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.26/12.24  all V_b_2 V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.26/12.24  all V_b_2 V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.26/12.24  all V_b_2 V_a_2 V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b_H))).
% 12.26/12.24  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_y))).
% 12.26/12.24  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_H),V_b))).
% 12.26/12.24  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_ya))).
% 12.26/12.24  all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z))).
% 12.26/12.24  all V_db_2 V_ca_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_ca_2!=V_db_2<->c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)))).
% 12.26/12.24  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))).
% 12.26/12.24  all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)).
% 12.26/12.24  all V_za_2 V_x_2 V_y_2 V_wa_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))<->V_wa_2=V_x_2|V_y_2=V_za_2)).
% 12.26/12.24  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))).
% 12.26/12.24  all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_w V_z2 V_z1 (hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_w))).
% 12.26/12.24  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all T_a (class_Groups_Osgn__if(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))).
% 12.26/12.24  all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.24  all 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_Oinverse(T_a,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)))).
% 12.26/12.24  all 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_Oinverse(T_a,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_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,V_b,V_a)))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.24  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_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  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_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_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_a)))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 12.26/12.24  all V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,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)))).
% 12.26/12.24  all 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_Oinverse(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)=c_Groups_Oone__class_Oone(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b)).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 12.26/12.24  all V_a T_a (class_Fields_Ofield(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  all V_y_2 V_x_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_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_d))))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m)=hAPP(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)).
% 12.26/12.24  all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m))=hAPP(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)).
% 12.26/12.24  all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(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)).
% 12.26/12.24  all V_y V_x (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y))).
% 12.26/12.24  all V_S V_R (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,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)))).
% 12.26/12.24  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_Groups_Osgn__class_Osgn(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (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_a)))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(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__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 12.26/12.24  all V_a T_a (class_Fields_Olinordered__field(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_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 12.26/12.24  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 12.26/12.24  all V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z))))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_x),V_y),V_z))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y))).
% 12.26/12.24  all V_x (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.24  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))).
% 12.26/12.24  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)))))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_y_2 V_x_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_y_2 V_x_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y)))).
% 12.26/12.24  all V_u V_y V_x1 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_x1)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)))))).
% 12.26/12.24  all V_u V_y V_x1 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_x1)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u))))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> ((all B_e (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e))))->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 12.26/12.24  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,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x)).
% 12.26/12.24  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)->hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,V_y)))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (hAPP(c_Transcendental_Oln,V_x_2)=hAPP(c_Transcendental_Oln,V_y_2)<->V_x_2=V_y_2))).
% 12.26/12.24  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,hAPP(c_Transcendental_Oln,V_x),V_x)).
% 12.26/12.24  hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)))).
% 12.26/12.24  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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_Oone__class_Oone(tc_RealDef_Oreal),V_x))).
% 12.26/12.24  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,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (hAPP(c_Transcendental_Oln,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))).
% 12.26/12.24  all V_a_2 V_wa_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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))))).
% 12.26/12.24  all V_wa_2 V_ca_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)))))).
% 12.26/12.24  all V_ca_2 V_b_2 V_wa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)))))).
% 12.26/12.24  all V_wa_2 V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))& (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)))))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)->c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_y_2 V_x_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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2))).
% 12.26/12.24  all V_y_2 V_x_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_x_2)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)<->V_x_2=V_y_2)).
% 12.26/12.24  all V_x_2 V_wa_2 T_a (class_Int_Onumber(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=V_x_2<->V_x_2=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))).
% 12.26/12.24  all V_z V_w V_v T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))),V_z)).
% 12.26/12.24  all V_w V_v T_a (class_Int_Onumber__ring(T_a)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))).
% 12.26/12.24  all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))=hAPP(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))).
% 12.26/12.24  all V_y_2 V_x_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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,V_y_2))).
% 12.26/12.24  all V_wa_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_wa_2))<-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)))).
% 12.26/12.24  all V_v V_b V_a T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))).
% 12.26/12.24  all V_c V_b V_v T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c))).
% 12.26/12.24  all V_wa_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_wa_2))<-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))=V_b_2)& (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_ca_2 V_b_2 V_wa_2 T_a (class_Fields_Ofield__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)=V_b_2)& (V_ca_2=c_Groups_Ozero__class_Ozero(T_a)->c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_wa_2 V_ca_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_ca_2)=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))& (V_ca_2=c_Groups_Ozero__class_Ozero(T_a)->c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_a_2 V_wa_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_wa_2))=V_a_2<-> (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))& (c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)->V_a_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_w T_b (class_Int_Onumber(T_b)&class_Rings_Odivision__ring(T_b)->c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w))=c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w))).
% 12.26/12.24  all V_a_2 V_wa_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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))))).
% 12.26/12.24  all V_wa_2 V_ca_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)))))).
% 12.26/12.24  all V_ca_2 V_b_2 V_wa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)))))).
% 12.26/12.24  all V_wa_2 V_b_2 V_a_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)&class_Int_Onumber(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))))& (-c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)))))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)->c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2))).
% 12.26/12.24  all V_x_2 V_ca_2 T_a (class_RealVector_Oreal__normed__field(T_a)->c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_a ((V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 12.26/12.24  all V_x ((V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 12.26/12.24  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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))).
% 12.26/12.24  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,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_w V_v (hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))).
% 12.26/12.24  all V_z V_w T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))),V_z)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_z)).
% 12.26/12.24  all V_w T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))).
% 12.26/12.24  all V_w T_a (class_Int_Onumber__ring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)).
% 12.26/12.24  all V_x T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x))).
% 12.26/12.24  all V_y_2 V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)=hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)<->V_x_2=V_y_2).
% 12.26/12.24  all T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_a_2)).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  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,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))).
% 12.26/12.24  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,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2))).
% 12.26/12.24  all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Oordered__ab__group__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_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))).
% 12.26/12.24  all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 12.26/12.24  all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2))).
% 12.26/12.24  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,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 12.26/12.24  all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y))).
% 12.26/12.24  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))).
% 12.26/12.24  all V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x))).
% 12.26/12.24  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 12.26/12.24  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 12.26/12.24  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)).
% 12.26/12.24  all V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))).
% 12.26/12.24  all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x).
% 12.26/12.24  all V_x_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)<->V_x_2=V_y_2)).
% 12.26/12.24  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2)).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_a_2=V_b_2)).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)).
% 12.26/12.24  all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.26/12.24  all V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z).
% 12.26/12.24  all V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z).
% 12.26/12.24  all V_z3 V_z2 V_z1 (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3)=hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3))).
% 12.26/12.24  all V_w V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)=hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z)).
% 12.26/12.24  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)).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_j)))).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)-> (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 12.26/12.24  c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 12.26/12.24  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 12.26/12.24  all V_za_2 V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)|V_wa_2=V_za_2).
% 12.26/12.24  all V_za_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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_w V_z2 V_z1 (hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w))).
% 12.26/12.24  all V_z2 V_z1 V_w (hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2))).
% 12.26/12.24  all V_za_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2)).
% 12.26/12.24  all V_za_2 V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_za_2)).
% 12.26/12.24  all V_za_2 V_wa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_wa_2 V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_za_2,V_wa_2)&V_za_2!=V_wa_2).
% 12.26/12.24  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))).
% 12.26/12.24  all V_x (hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))=V_x).
% 12.26/12.24  all V_x V_u (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u)=V_x->hAPP(c_Transcendental_Oln,V_x)=V_u).
% 12.26/12.24  all V_x V_y (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)=V_x->hAPP(c_Transcendental_Oln,V_x)=V_y).
% 12.26/12.24  all V_x T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->hAPP(c_Transcendental_Oexp(T_a),V_x)!=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_x_2 T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2))).
% 12.26/12.24  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_Ouminus__class_Ouminus(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))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2))).
% 12.26/12.24  all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2))).
% 12.26/12.24  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.24  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b)).
% 12.26/12.24  all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)).
% 12.26/12.24  all V_x_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 12.26/12.24  all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 12.26/12.24  all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))).
% 12.26/12.24  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 12.26/12.24  all V_x V_u c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x)).
% 12.26/12.24  all V_y_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.24  all V_a_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=V_a_2).
% 12.26/12.24  all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.24  all V_x (-c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.24  all V_x (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.24  all T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.24  all V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y))).
% 12.26/12.24  all V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)&class_SEQ_Obanach(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y))=hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)).
% 12.26/12.24  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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))=V_x).
% 12.26/12.24  all V_x_2 (hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))=V_x_2<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)).
% 12.26/12.24  all V_E_2 V_D_2 V_x_2 V_f_2 T_a (class_RealVector_Oreal__normed__field(T_a)-> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)->V_D_2=V_E_2))).
% 12.26/12.24  all V_Y_2 V_X_2 V_x_2 V_f_2 T_a (class_RealVector_Oreal__normed__field(T_a)-> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2)-> (V_X_2=V_Y_2->c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2)))).
% 12.26/12.24  all V_E_2 V_D_2 V_x_2 V_f_2 T_a (class_RealVector_Oreal__normed__field(T_a)-> (c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)-> (V_D_2=V_E_2->c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)))).
% 12.26/12.24  all V_x T_a (class_Groups_Osgn__if(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(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_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))).
% 12.26/12.24  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 12.26/12.24  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x))).
% 12.26/12.24  all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (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,V_q_H,V_q))))))).
% 12.26/12.24  all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))).
% 12.26/12.24  all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)-> (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)-> (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,V_q,V_q_H))))))).
% 12.26/12.24  all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))).
% 12.26/12.24  all V_w (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 12.26/12.24  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.24  all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 12.26/12.24  all V_w V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w))).
% 12.26/12.24  all V_i ((V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (V_i!=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_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 12.26/12.24  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.24  all V_w V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 12.26/12.24  c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.24  all V_k (c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k)=V_k).
% 12.26/12.24  all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 12.26/12.24  all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)))).
% 12.26/12.24  all V_r_H V_q_H V_b_H (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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)))).
% 12.26/12.24  all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),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_r_H)-> (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_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 12.26/12.24  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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x),V_y)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Int_Onumber__ring(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))))).
% 12.26/12.24  all V_l_2 V_x_2 V_f_2 (c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_h (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)))))))))).
% 12.26/12.24  all V_l_2 V_x_2 V_f_2 (c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_h (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2))))))))).
% 12.26/12.24  all V_za_2 T_a (class_Rings_Osemiring__1(T_a)-> (c_Int_Oiszero(T_a,V_za_2)<->V_za_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all T_a (class_Rings_Osemiring__1(T_a)->c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all T_a (class_Rings_Osemiring__1(T_a)-> -c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))).
% 12.26/12.24  all V_x_2 T_a (class_Int_Onumber__ring(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))))).
% 12.26/12.24  all V_y_2 T_a (class_Int_Onumber__ring(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))))).
% 12.26/12.24  all V_w T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)=c_Int_OPls.
% 12.26/12.24  c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.24  c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls).
% 12.26/12.24  c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.24  all V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls)=V_k).
% 12.26/12.24  all V_k (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k)=V_k).
% 12.26/12.24  -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 12.26/12.24  all V_w (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w)=c_Int_OPls).
% 12.26/12.24  c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 12.26/12.24  all V_x (c_Int_Osucc(c_Int_Opred(V_x))=V_x).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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).
% 12.26/12.24  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).
% 12.26/12.24  -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.24  c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls).
% 12.26/12.24  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))))).
% 12.26/12.24  all V_k V_v_H V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k))=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k))).
% 12.26/12.24  all V_v_H V_v ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->hAPP(c_Groups_Otimes__class_Otimes(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_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)->hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H)))).
% 12.26/12.24  all T_a (class_Int_Onumber__ring(T_a)->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_y_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_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_y_2))).
% 12.26/12.24  all V_x_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_x_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OPls))).
% 12.26/12.24  all V_y_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_y_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2))).
% 12.26/12.24  all V_x_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_x_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_x_2 T_a (class_Int_Onumber__ring(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))))).
% 12.26/12.24  all V_y_2 T_a (class_Int_Onumber__ring(T_a)-> (c_Groups_Oone__class_Oone(T_a)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))))).
% 12.26/12.24  c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.24  c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.24  all V_l (c_Int_OPls!=c_Int_OBit1(V_l)).
% 12.26/12.24  all V_k (c_Int_OBit1(V_k)!=c_Int_OPls).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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).
% 12.26/12.24  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)).
% 12.26/12.24  all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_k (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k))=c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)))).
% 12.26/12.24  all V_w T_a (class_Int_Onumber__ring(T_a)&class_Int_Oring__char__0(T_a)-> -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)))).
% 12.26/12.24  c_Int_Osucc(c_Int_OPls)=c_Int_OBit1(c_Int_OPls).
% 12.26/12.24  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))).
% 12.26/12.24  all V_a T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a)=V_a).
% 12.26/12.24  all V_a T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_a).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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).
% 12.26/12.24  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).
% 12.26/12.24  all T_a (class_Fields_Ofield(T_a)&class_Int_Onumber__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.24  all T_a (class_Int_Onumber__ring(T_a)-> -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_y_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_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2))).
% 12.26/12.24  all V_x_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_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.24  all V_y_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_y_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2))).
% 12.26/12.24  all V_x_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_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.26/12.24  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.26/12.24  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.26/12.24  all V_n_2 V_ma_2 (V_ma_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.26/12.24  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 12.26/12.24  all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 12.26/12.24  all V_P_2 V_n_2 V_ma_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))-> ((V_ma_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)<->V_ma_2=V_n_2).
% 12.26/12.24  all V_n_2 V_k_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)<->V_ma_2=V_n_2).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.26/12.24  all V_k V_n V_m (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k))).
% 12.26/12.24  all V_n V_m (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m)).
% 12.26/12.24  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.26/12.24  all V_n_2 (V_n_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_n_2)).
% 12.26/12.24  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 12.26/12.24  all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 12.26/12.24  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.26/12.24  all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_n_2 V_k_2 V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)<->V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)<->V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_n_2 V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_m (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_n (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)&V_ma_2!=V_n_2).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)<-> (exists B_k (V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)))).
% 12.26/12.24  all V_n_2 V_ma_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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_k V_n V_m (hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k))).
% 12.26/12.24  all V_n V_m V_k (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n))).
% 12.26/12.24  all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)).
% 12.26/12.24  all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_l)))).
% 12.26/12.24  all V_n_2 V_ma_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.26/12.24  all V_n (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.26/12.24  all V_n (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n).
% 12.26/12.24  all V_n_2 V_ma_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_ma_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.26/12.24  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.26/12.24  all V_n_2 V_k_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.26/12.24  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_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)))).
% 12.26/12.24  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_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)))).
% 12.26/12.24  all V_n V_m (V_m=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  all V_n_2 V_k_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)<->V_ma_2=V_n_2)).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.26/12.24  all V_n_2 V_ma_2 V_k_2 (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2).
% 12.26/12.24  all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k)).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls).
% 12.26/12.24  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)))))).
% 12.26/12.24  all V_k_2 V_P_2 V_db_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_2)-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_db_2)))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2))))))))).
% 12.26/12.24  all V_wa_2 T_a (class_Int_Onumber__ring(T_a)&class_Int_Oring__char__0(T_a)-> (c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))<->c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))).
% 12.26/12.24  all V_k (c_Int_Opred(c_Int_OBit1(V_k))=c_Int_OBit0(V_k)).
% 12.26/12.24  all V_k (c_Int_Opred(c_Int_OBit0(V_k))=c_Int_OBit1(c_Int_Opred(V_k))).
% 12.26/12.24  all V_k (c_Int_Osucc(c_Int_OBit0(V_k))=c_Int_OBit1(V_k)).
% 12.26/12.24  all V_k (c_Int_Osucc(c_Int_OBit1(V_k))=c_Int_OBit0(c_Int_Osucc(V_k))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_l V_k (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l)=c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_k (c_Int_OBit0(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_l V_k (c_Int_OBit1(V_k)!=c_Int_OBit0(V_l)).
% 12.26/12.24  all V_l V_k (c_Int_OBit0(V_k)!=c_Int_OBit1(V_l)).
% 12.26/12.24  all V_k (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k))=c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))).
% 12.26/12.24  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).
% 12.26/12.24  all V_k_2 (c_Int_OBit0(V_k_2)=c_Int_OPls<->V_k_2=c_Int_OPls).
% 12.26/12.24  all V_l_2 (c_Int_OPls=c_Int_OBit0(V_l_2)<->c_Int_OPls=V_l_2).
% 12.26/12.24  c_Int_OBit0(c_Int_OPls)=c_Int_OPls.
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_l V_k (hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k)),V_l)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l)).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_w T_a (class_Int_Onumber__ring(T_a)->hAPP(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))),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_za_2 V_y_2 V_x_2 (V_x_2=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))<->hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2)).
% 12.26/12.24  all V_z T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)).
% 12.26/12.24  all V_z T_a (class_Int_Onumber__ring(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z)=c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_z (hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)).
% 12.26/12.24  all V_z (hAPP(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_z)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)).
% 12.26/12.24  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))).
% 12.26/12.24  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)))))).
% 12.26/12.24  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)).
% 12.26/12.24  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))))))).
% 12.26/12.24  all V_r_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_r_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_r_2))).
% 12.26/12.24  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))).
% 12.26/12.24  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).
% 12.26/12.24  all V_D_2 V_x_2 (V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)->V_D_2=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),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_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->V_D_2=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))->c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2)))).
% 12.26/12.24  all V_k_2 V_v_2 V_b_2 V_a_2 (V_a_2!=V_b_2-> ((all B_x c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,B_x,V_k_2))->hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.26/12.24  all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)).
% 12.26/12.24  all V_y_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.26/12.24  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),hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  all V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<->V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.24  hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.24  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,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)).
% 12.26/12.24  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,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)).
% 12.26/12.24  all V_y V_x (hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y))=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y))).
% 12.26/12.24  all V_x (hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  all V_x (hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  all V_y V_x (hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))).
% 12.26/12.24  all V_y_2 V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2)=hAPP(c_NthRoot_Osqrt,V_y_2)<->V_x_2=V_y_2).
% 12.26/12.24  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),hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->hAPP(c_NthRoot_Osqrt,V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_y_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)).
% 12.26/12.24  all V_y_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  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),hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (hAPP(c_NthRoot_Osqrt,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  all V_x_2 (hAPP(c_NthRoot_Osqrt,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.24  hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.24  all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))).
% 12.26/12.24  all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x)=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))).
% 12.26/12.24  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  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,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u)).
% 12.26/12.24  all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)->c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 12.26/12.24  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,hAPP(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)))))).
% 12.26/12.24  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),hAPP(c_NthRoot_Osqrt,hAPP(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)))))))).
% 12.26/12.24  all V_k V_x (hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(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))).
% 12.26/12.24  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q)=c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p),V_q))).
% 12.26/12.24  all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q)=hAPP(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))).
% 12.26/12.24  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).
% 12.26/12.24  all V_wa_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_wa_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_wa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a)).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x)=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))))).
% 12.26/12.24  all V_a T_a (class_Groups_Omonoid__mult(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))))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)).
% 12.26/12.24  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)).
% 12.26/12.24  all V_a T_a (class_Rings_Oring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(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))))).
% 12.26/12.24  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  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)))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_w T_b (class_Groups_Omonoid__mult(T_b)&class_Int_Onumber(T_b)->c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w))).
% 12.26/12.24  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_Oone__class_Oone(T_a)<->V_a_2=c_Groups_Oone__class_Oone(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 12.26/12.24  all V_n V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,hAPP(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))=hAPP(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))).
% 12.26/12.24  all V_n V_a T_a (class_Rings_Oring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),hAPP(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_Power_Opower__class_Opower(T_a,V_a,hAPP(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))).
% 12.26/12.24  all V_y_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.24  all V_x (hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_x V_u c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,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_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))))))).
% 12.26/12.24  all V_y_2 V_x_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_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_y_2 V_x_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_x_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_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_y V_x T_a (class_Int_Onumber__ring(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,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(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))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))).
% 12.26/12.24  all V_k V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_k)),c_Groups_Ozero__class_Ozero(T_a))->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  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,V_a,hAPP(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)))).
% 12.26/12.24  all V_n T_a (class_Rings_Oring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(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_Oone__class_Oone(T_a)).
% 12.26/12.24  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)->hAPP(c_NthRoot_Osqrt,V_x)=V_y)).
% 12.26/12.24  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,hAPP(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).
% 12.26/12.24  all V_x_2 (c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_x_2<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)).
% 12.26/12.24  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,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 12.26/12.24  all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(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))))))).
% 12.26/12.24  all V_x V_y c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y,hAPP(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))))))).
% 12.26/12.24  all V_d V_b V_c V_a c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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,hAPP(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)))))),hAPP(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)))))))).
% 12.26/12.24  all V_y V_x (hAPP(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)).
% 12.26/12.24  all V_y V_x (hAPP(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)).
% 12.26/12.24  all V_ya V_xa V_y V_x (c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(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))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(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))))))).
% 12.26/12.24  all V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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))))))).
% 12.26/12.24  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)).
% 12.26/12.24  all V_y V_x (c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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_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))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))).
% 12.26/12.24  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)))))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n_2 V_x_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_x_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.24  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))).
% 12.26/12.24  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))=hAPP(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))).
% 12.26/12.24  all V_z V_y V_x (c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z)=c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z))).
% 12.26/12.24  all V_n_2 V_x_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_x_2,V_n_2))<->V_n_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_x_2)).
% 12.26/12.24  all V_wa_2 V_x_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_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))<->c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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_x_2)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n)=hAPP(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))).
% 12.26/12.24  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))).
% 12.26/12.24  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)).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n))=c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n)).
% 12.26/12.24  all V_n V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n)).
% 12.26/12.24  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).
% 12.26/12.24  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)))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)))).
% 12.26/12.24  all V_n_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_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.26/12.24  all V_n_2 V_ma_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_ma_2)=c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)<->V_ma_2=V_n_2))).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  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))=hAPP(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))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_n V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n))).
% 12.26/12.24  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)))).
% 12.26/12.24  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))))).
% 12.26/12.24  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))))).
% 12.26/12.24  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))).
% 12.26/12.24  all V_n V_a T_a (class_Rings_Oring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n))).
% 12.26/12.24  all V_y_2 V_x_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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n))))).
% 12.26/12.24  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)))))).
% 12.26/12.24  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))))).
% 12.26/12.24  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)))))).
% 12.26/12.24  all V_y_2 V_x_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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2)))).
% 12.26/12.24  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)))).
% 12.26/12.24  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))))).
% 12.26/12.24  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).
% 12.26/12.24  all V_x (hAPP(c_Transcendental_Oarctan,V_x)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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))))))))))).
% 12.26/12.24  hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.24  all V_x (hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x))).
% 12.26/12.24  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,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y))).
% 12.26/12.24  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,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y))).
% 12.26/12.24  all V_x_2 c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))).
% 12.26/12.24  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,hAPP(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)).
% 12.26/12.24  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,hAPP(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,hAPP(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,hAPP(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))).
% 12.26/12.24  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))).
% 12.26/12.24  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)).
% 12.26/12.24  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,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n))=c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))).
% 12.26/12.24  all V_y V_x V_c (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.26/12.24  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)->hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x)))).
% 12.26/12.24  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(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)))).
% 12.26/12.24  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_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 12.26/12.24  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_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 12.26/12.24  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 12.26/12.24  all V_a T_a (class_Groups_Oabs__if(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))& (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 12.26/12.24  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)))).
% 12.26/12.24  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)).
% 12.26/12.24  all V_x (c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))).
% 12.26/12.24  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,hAPP(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)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_d))))).
% 12.26/12.24  all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 12.26/12.24  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 12.26/12.24  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 12.26/12.24  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 12.26/12.24  all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 12.26/12.24  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.26/12.24  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__semiring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oordered__semiring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 12.26/12.24  class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__ring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.26/12.24  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.26/12.24  class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oab__group__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oordered__ring(tc_Int_Oint).
% 12.26/12.24  class_Orderings_Opreorder(tc_Int_Oint).
% 12.26/12.24  class_Orderings_Olinorder(tc_Int_Oint).
% 12.26/12.24  class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.26/12.24  class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.26/12.24  class_Groups_Omonoid__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Osemiring__1(tc_Int_Oint).
% 12.26/12.24  class_Rings_Osemiring__0(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ogroup__add(tc_Int_Oint).
% 12.26/12.24  class_Rings_Omult__zero(tc_Int_Oint).
% 12.26/12.24  class_Orderings_Oorder(tc_Int_Oint).
% 12.26/12.24  class_Int_Oring__char__0(tc_Int_Oint).
% 12.26/12.24  class_Int_Onumber__ring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Osemiring(tc_Int_Oint).
% 12.26/12.24  class_Orderings_Oord(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ouminus(tc_Int_Oint).
% 12.26/12.24  class_Groups_Osgn__if(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oabs__if(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oring__1(tc_Int_Oint).
% 12.26/12.24  class_Power_Opower(tc_Int_Oint).
% 12.26/12.24  class_Groups_Ozero(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oring(tc_Int_Oint).
% 12.26/12.24  class_Rings_Oidom(tc_Int_Oint).
% 12.26/12.24  class_Int_Onumber(tc_Int_Oint).
% 12.26/12.24  class_Groups_Oone(tc_Int_Oint).
% 12.26/12.24  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Oordered__semiring(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.26/12.24  class_Orderings_Opreorder(tc_Nat_Onat).
% 12.26/12.24  class_Orderings_Olinorder(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Osemiring__1(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Osemiring__0(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Omult__zero(tc_Nat_Onat).
% 12.26/12.24  class_Orderings_Oorder(tc_Nat_Onat).
% 12.26/12.24  class_Rings_Osemiring(tc_Nat_Onat).
% 12.26/12.24  class_Orderings_Oord(tc_Nat_Onat).
% 12.26/12.24  class_Power_Opower(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Ozero(tc_Nat_Onat).
% 12.26/12.24  class_Int_Onumber(tc_Nat_Onat).
% 12.26/12.24  class_Groups_Oone(tc_Nat_Onat).
% 12.26/12.24  class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 12.26/12.24  class_Orderings_Opreorder(tc_HOL_Obool).
% 12.26/12.24  class_Orderings_Oorder(tc_HOL_Obool).
% 12.26/12.24  class_Orderings_Oord(tc_HOL_Obool).
% 12.26/12.24  class_Groups_Ouminus(tc_HOL_Obool).
% 12.26/12.24  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.26/12.24  class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.26/12.24  class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.24  class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 12.26/12.24  class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 12.26/12.24  class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.26/12.24  class_RealVector_Oreal__normed__field(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 12.26/12.24  class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Fields_Olinordered__field(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.26/12.24  class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.26/12.24  class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 12.26/12.24  class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.26/12.25  class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.26/12.25  class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.26/12.25  class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.26/12.25  class_Int_Onumber__ring(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.26/12.25  class_Orderings_Oord(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Ouminus(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Osgn__if(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Oabs__if(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.26/12.25  class_Fields_Ofield(tc_RealDef_Oreal).
% 12.26/12.25  class_Power_Opower(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  class_SEQ_Obanach(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Oring(tc_RealDef_Oreal).
% 12.26/12.25  class_Rings_Oidom(tc_RealDef_Oreal).
% 12.26/12.25  class_Int_Onumber(tc_RealDef_Oreal).
% 12.26/12.25  class_Groups_Oone(tc_RealDef_Oreal).
% 12.26/12.25  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 12.26/12.25  class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 12.26/12.25  class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 12.26/12.25  class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.25  class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 12.26/12.25  class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Osemiring__1(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 12.26/12.25  class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 12.26/12.25  class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Osemiring(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ouminus(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Oring__1(tc_Complex_Ocomplex).
% 12.26/12.25  class_Fields_Ofield(tc_Complex_Ocomplex).
% 12.26/12.25  class_Power_Opower(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Ozero(tc_Complex_Ocomplex).
% 12.26/12.25  class_SEQ_Obanach(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Oring(tc_Complex_Ocomplex).
% 12.26/12.25  class_Rings_Oidom(tc_Complex_Ocomplex).
% 12.26/12.25  class_Int_Onumber(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Oone(tc_Complex_Ocomplex).
% 12.26/12.25  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Ozero__ne_q__one(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Power_Opower(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Int_Onumber(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  class_Groups_Oone(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.25  -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e).
% 12.26/12.25  end_of_list.
% 12.26/12.25  
% 12.26/12.25  -------> usable clausifies to:
% 12.26/12.25  
% 12.26/12.25  list(usable).
% 12.26/12.25  0 [] A=A.
% 12.26/12.25  0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)).
% 12.26/12.25  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,v_m____)).
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z).
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____).
% 12.26/12.25  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)=V_a.
% 12.26/12.25  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x)=V_x.
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a).
% 12.26/12.25  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ry)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 12.26/12.25  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_b_2)|V_a_2=V_b_2.
% 12.26/12.25  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_b_2)|V_a_2!=V_b_2.
% 12.26/12.25  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2),V_ca_2)|V_a_2=V_b_2.
% 12.26/12.25  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2),V_ca_2)|V_a_2!=V_b_2.
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_y)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_ry)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_ry)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx)=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ly).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_rx)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ry).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c1).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)).
% 12.26/12.25  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),hAPP(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)).
% 12.26/12.25  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),hAPP(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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  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,hAPP(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)).
% 12.26/12.25  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,hAPP(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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  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_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  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_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  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_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  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_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a)|V_za_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2).
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a)|V_za_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)!=V_a_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)!=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)=V_b_2.
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)!=V_b_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|V_b!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c)|c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)!=V_a_2|V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)=V_b_2.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)!=V_b_2.
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_m),V_n)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(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).
% 12.26/12.25  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)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Omult__zero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Omult__zero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c).
% 12.26/12.25  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.
% 12.26/12.25  0 [] c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 12.26/12.25  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 12.26/12.25  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 12.26/12.25  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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_x_2,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_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_y_2).
% 12.26/12.25  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_x_2,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.25  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_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_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_x_2).
% 12.26/12.25  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_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.25  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_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.25  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_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(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).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x),V_x).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_x).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_ca_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).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  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__e_q(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z).
% 12.26/12.25  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__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,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_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,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_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,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_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 12.26/12.25  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(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f2(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f2(V_g_2,V_f_2,T_a,T_b))).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),$f3(V_y,V_x,T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,$f3(V_y,V_x,T_a),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,$f3(V_y,V_x,T_a)),V_x),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(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_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 12.26/12.25  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_a_2=V_b_2.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_a_2!=V_b_2.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=V_b.
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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_ca_2)|V_b_2=V_ca_2.
% 12.26/12.25  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_ca_2)|V_b_2!=V_ca_2.
% 12.26/12.25  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_ca_2,V_a_2)|V_b_2=V_ca_2.
% 12.26/12.25  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_ca_2,V_a_2)|V_b_2!=V_ca_2.
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|V_a=V_b.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a).
% 12.26/12.25  0 [] c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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.
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b_H)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_y)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_H),V_b)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_ya)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z)).
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2=V_b_2|V_ca_2=V_db_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_ca_2!=V_db_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m).
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))|V_wa_2=V_x_2|V_y_2=V_za_2.
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))|V_wa_2!=V_x_2.
% 12.26/12.25  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))|V_y_2!=V_za_2.
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)).
% 12.26/12.25  0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  0 [] hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_w)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Osgn__if(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,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)).
% 12.26/12.25  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_Oinverse(T_a,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  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_Oinverse(T_a,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_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,V_b,V_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  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_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_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_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,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)).
% 12.26/12.25  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_Oinverse(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  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_Oinverse(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)!=c_Groups_Oone__class_Oone(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b.
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_d)).
% 12.26/12.25  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))).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m)=hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m))=hAPP(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).
% 12.26/12.25  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(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).
% 12.26/12.25  0 [] c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y)).
% 12.26/12.25  0 [] c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S)).
% 12.26/12.25  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,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)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -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_a).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(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__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(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_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.25  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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))).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_x),V_y),V_z).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y).
% 12.26/12.25  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  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).
% 12.26/12.25  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)))).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y))).
% 12.26/12.25  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_x1)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))).
% 12.26/12.25  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_x1)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),$f4(V_y,V_x,T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,$f4(V_y,V_x,T_a)))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.26/12.25  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,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x).
% 12.26/12.25  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)|hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,V_y)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|hAPP(c_Transcendental_Oln,V_x_2)!=hAPP(c_Transcendental_Oln,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|hAPP(c_Transcendental_Oln,V_x_2)=hAPP(c_Transcendental_Oln,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  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,hAPP(c_Transcendental_Oln,V_x),V_x).
% 12.26/12.25  0 [] hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_Oone__class_Oone(tc_RealDef_Oreal),V_x).
% 12.26/12.25  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,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|hAPP(c_Transcendental_Oln,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|hAPP(c_Transcendental_Oln,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2).
% 12.26/12.25  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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=V_x_2|V_x_2=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2).
% 12.26/12.25  0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=V_x_2|V_x_2!=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))),V_z).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))=hAPP(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)).
% 12.26/12.25  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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,V_y_2).
% 12.26/12.25  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_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,V_y_2).
% 12.26/12.25  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_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)).
% 12.26/12.25  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_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)).
% 12.26/12.25  0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))).
% 12.26/12.25  0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)).
% 12.26/12.25  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_wa_2))|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))=V_b_2.
% 12.26/12.25  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_wa_2))|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))!=V_b_2|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)=V_b_2.
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)!=V_b_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)!=V_b_2|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)=c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))!=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  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_wa_2))!=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))=V_a_2|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))=V_a_2|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  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_wa_2))=V_a_2|V_b_2!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Int_Onumber(T_b)| -class_Rings_Odivision__ring(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w))=c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(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_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_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)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2).
% 12.26/12.25  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)).
% 12.26/12.25  0 [] V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  0 [] V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.25  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.25  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.25  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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))),V_z)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_z).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)).
% 12.26/12.25  0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)).
% 12.26/12.25  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)!=hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)=hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)=V_a_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_a_2.
% 12.26/12.25  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__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_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)).
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 12.26/12.25  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 12.26/12.25  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2)!=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2)|V_a_2!=V_b_2.
% 12.26/12.25  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 12.26/12.25  0 [] -class_Rings_Oring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b).
% 12.26/12.25  0 [] -class_Rings_Oring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 12.26/12.25  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b).
% 12.26/12.25  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x)).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 12.26/12.25  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 12.26/12.25  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 12.26/12.25  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 12.26/12.25  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x.
% 12.26/12.25  0 [] -class_Groups_Ouminus(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)).
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2=V_y_2.
% 12.26/12.25  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)!=V_a_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2=V_b_2.
% 12.26/12.25  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2!=V_b_2.
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y).
% 12.26/12.25  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.
% 12.26/12.25  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).
% 12.26/12.25  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).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3)=hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3)).
% 12.26/12.25  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)=hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z).
% 12.26/12.25  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).
% 12.26/12.25  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_j)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_ma_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  0 [] c_Int_Osucc(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.26/12.25  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 12.26/12.25  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)|V_wa_2=V_za_2.
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_wa_2!=V_za_2.
% 12.26/12.25  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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.25  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_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.25  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)).
% 12.26/12.25  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).
% 12.26/12.25  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)).
% 12.26/12.25  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)).
% 12.26/12.25  0 [] hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w)).
% 12.26/12.25  0 [] hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2)).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_za_2).
% 12.26/12.25  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_za_2).
% 12.26/12.25  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_za_2,V_wa_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)|V_za_2!=V_wa_2.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_za_2,V_wa_2)|V_za_2=V_wa_2.
% 12.26/12.26  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)).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))=V_x.
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u)!=V_x|hAPP(c_Transcendental_Oln,V_x)=V_u.
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)!=V_x|hAPP(c_Transcendental_Oln,V_x)=V_y.
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|hAPP(c_Transcendental_Oexp(T_a),V_x)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2)).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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).
% 12.26/12.26  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(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_a_2).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b.
% 12.26/12.26  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x).
% 12.26/12.26  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.26  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 12.26/12.26  0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 12.26/12.26  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x)).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_a_2.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=V_a_2.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -class_SEQ_Obanach(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y))=hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 12.26/12.26  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,V_x_2,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 12.26/12.26  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,V_x_2,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))=V_x.
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))!=V_x_2|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))=V_x_2| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)|V_D_2=V_E_2.
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2)|V_X_2!=V_Y_2|c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2).
% 12.26/12.26  0 [] -class_RealVector_Oreal__normed__field(T_a)| -c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)|V_D_2!=V_E_2|c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2).
% 12.26/12.26  0 [] -class_Groups_Osgn__if(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Osgn__if(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_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.26  0 [] -class_Groups_Osgn__if(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_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x)).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -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,V_q_H,V_q).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)| -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)| -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,V_q,V_q_H).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)).
% 12.26/12.26  0 [] V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.26  0 [] V_i=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_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.26  0 [] V_i=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_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 12.26/12.26  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.26/12.26  0 [] c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k)=V_k.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q).
% 12.26/12.26  0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -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,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),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_r_H)| -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_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x),V_y)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f5(V_l_2,V_x_2,V_f_2)).
% 12.26/12.26  0 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,$f5(V_l_2,V_x_2,V_f_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h))).
% 12.26/12.26  0 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f6(V_l_2,V_x_2,V_f_2)).
% 12.26/12.26  0 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,$f6(V_l_2,V_x_2,V_f_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2)).
% 12.26/12.26  0 [] -class_Rings_Osemiring__1(T_a)| -c_Int_Oiszero(T_a,V_za_2)|V_za_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Rings_Osemiring__1(T_a)|c_Int_Oiszero(T_a,V_za_2)|V_za_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Rings_Osemiring__1(T_a)|c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Rings_Osemiring__1(T_a)| -c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)=c_Int_OPls.
% 12.26/12.26  0 [] c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.26/12.26  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls).
% 12.26/12.26  0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls)=V_k.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k)=V_k.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w)=c_Int_OPls.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 12.26/12.26  0 [] c_Int_Osucc(c_Int_Opred(V_x))=V_x.
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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.
% 12.26/12.26  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.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k))=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(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_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_y_2).
% 12.26/12.26  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_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OPls,V_y_2).
% 12.26/12.26  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_x_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OPls).
% 12.26/12.26  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_x_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OPls).
% 12.26/12.26  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_y_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2).
% 12.26/12.26  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_y_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2).
% 12.26/12.26  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_x_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls).
% 12.26/12.26  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_x_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)!=c_Groups_Oone__class_Oone(T_a)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oone__class_Oone(T_a)=c_Int_Onumber__class_Onumber__of(T_a,V_y_2)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))).
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  0 [] c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Int_OPls!=c_Int_OBit1(V_l).
% 12.26/12.26  0 [] c_Int_OBit1(V_k)!=c_Int_OPls.
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Int_OBit1(V_k_2)!=c_Int_OBit1(V_l_2)|V_k_2=V_l_2.
% 12.26/12.26  0 [] c_Int_OBit1(V_k_2)=c_Int_OBit1(V_l_2)|V_k_2!=V_l_2.
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k))=c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))).
% 12.26/12.26  0 [] c_Int_Osucc(c_Int_OPls)=c_Int_OBit1(c_Int_OPls).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a)=V_a.
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=V_a.
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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.
% 12.26/12.26  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.
% 12.26/12.26  0 [] -class_Fields_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))).
% 12.26/12.26  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)))).
% 12.26/12.26  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_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2).
% 12.26/12.26  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_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2).
% 12.26/12.26  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_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  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_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  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_y_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2).
% 12.26/12.26  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_y_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2).
% 12.26/12.26  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_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  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_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  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))).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.26/12.26  0 [] V_ma_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 12.26/12.26  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_ma_2=V_n_2.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2=V_n_2.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2!=V_n_2.
% 12.26/12.26  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.
% 12.26/12.26  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).
% 12.26/12.26  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.26  0 [] V_n_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_n_2).
% 12.26/12.26  0 [] V_n_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_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)|V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 12.26/12.26  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).
% 12.26/12.26  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2.
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,$f7(V_n_2,V_ma_2)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_l)).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)|V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 12.26/12.26  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_ma_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.26/12.26  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_ma_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2).
% 12.26/12.26  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_ma_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)).
% 12.26/12.26  0 [] V_m!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_ma_2=V_n_2.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2.
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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,$f8(V_l_2,V_k_2)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 12.26/12.26  0 [] c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)).
% 12.26/12.26  0 [] c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)=c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls).
% 12.26/12.26  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -class_Int_Onumber__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_2)|hBOOL(hAPP(V_P_2,$f9(V_k_2,V_P_2,V_db_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2)))).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_2)| -hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,$f9(V_k_2,V_P_2,V_db_2),V_db_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2)))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))| -c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)).
% 12.26/12.26  0 [] c_Int_Opred(c_Int_OBit1(V_k))=c_Int_OBit0(V_k).
% 12.26/12.26  0 [] c_Int_Opred(c_Int_OBit0(V_k))=c_Int_OBit1(c_Int_Opred(V_k)).
% 12.26/12.26  0 [] c_Int_Osucc(c_Int_OBit0(V_k))=c_Int_OBit1(V_k).
% 12.26/12.26  0 [] c_Int_Osucc(c_Int_OBit1(V_k))=c_Int_OBit0(c_Int_Osucc(V_k)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l)=c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Int_OBit0(V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] c_Int_OBit1(V_k)!=c_Int_OBit0(V_l).
% 12.26/12.26  0 [] c_Int_OBit0(V_k)!=c_Int_OBit1(V_l).
% 12.26/12.26  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k))=c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)).
% 12.26/12.26  0 [] c_Int_OBit0(V_k_2)!=c_Int_OBit0(V_l_2)|V_k_2=V_l_2.
% 12.26/12.26  0 [] c_Int_OBit0(V_k_2)=c_Int_OBit0(V_l_2)|V_k_2!=V_l_2.
% 12.26/12.26  0 [] c_Int_OBit0(V_k_2)!=c_Int_OPls|V_k_2=c_Int_OPls.
% 12.26/12.26  0 [] c_Int_OBit0(V_k_2)=c_Int_OPls|V_k_2!=c_Int_OPls.
% 12.26/12.26  0 [] c_Int_OPls!=c_Int_OBit0(V_l_2)|c_Int_OPls=V_l_2.
% 12.26/12.26  0 [] c_Int_OPls=c_Int_OBit0(V_l_2)|c_Int_OPls!=V_l_2.
% 12.26/12.26  0 [] c_Int_OBit0(c_Int_OPls)=c_Int_OPls.
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k)),V_l)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l).
% 12.26/12.26  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))).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|hAPP(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))),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)).
% 12.26/12.26  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))).
% 12.26/12.26  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))).
% 12.26/12.26  0 [] V_x_2!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2).
% 12.26/12.26  0 [] V_x_2=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2)!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(T_a,V_z,V_z).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z)=c_Groups_Oplus__class_Oplus(T_a,V_z,V_z).
% 12.26/12.26  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))).
% 12.26/12.26  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)))).
% 12.26/12.26  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)))).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z).
% 12.26/12.26  0 [] hAPP(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_z)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z).
% 12.26/12.26  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))).
% 12.26/12.26  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))))).
% 12.26/12.26  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).
% 12.26/12.26  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))))).
% 12.26/12.26  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_r_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_r_2).
% 12.26/12.26  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_r_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_r_2).
% 12.26/12.26  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).
% 12.26/12.26  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.
% 12.26/12.26  0 [] V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2).
% 12.26/12.26  0 [] V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|V_D_2!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2).
% 12.26/12.26  0 [] V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_D_2!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),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_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2).
% 12.26/12.26  0 [] V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_D_2!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|V_D_2!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2).
% 12.26/12.26  0 [] V_a_2=V_b_2| -c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,$f10(V_k_2,V_v_2,V_b_2,V_a_2),V_k_2)|hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.26/12.26  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),hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.26  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,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y))=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y)).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)!=hAPP(c_NthRoot_Osqrt,V_y_2)|V_x_2=V_y_2.
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)=hAPP(c_NthRoot_Osqrt,V_y_2)|V_x_2!=V_y_2.
% 12.26/12.26  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),hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|hAPP(c_NthRoot_Osqrt,V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.26/12.26  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),hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|hAPP(c_NthRoot_Osqrt,V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x)=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  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,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  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,hAPP(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).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(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)))))))).
% 12.26/12.26  0 [] hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k))=c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(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)).
% 12.26/12.26  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q)=c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p),V_q)).
% 12.26/12.26  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q)=hAPP(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)).
% 12.26/12.26  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.
% 12.26/12.26  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_wa_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_wa_2))!=c_Groups_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_wa_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_wa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x)=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)))).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(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))))=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Oring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(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)))).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.26  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))))).
% 12.26/12.26  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).
% 12.26/12.26  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.
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_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_y_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_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_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_y_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_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(T_b)| -class_Int_Onumber(T_b)|c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)).
% 12.26/12.26  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_Oone__class_Oone(T_a)|V_a_2=c_Groups_Oone__class_Oone(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  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_Oone__class_Oone(T_a)|V_a_2!=c_Groups_Oone__class_Oone(T_a).
% 12.26/12.26  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_Oone__class_Oone(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 12.26/12.26  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,hAPP(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))=hAPP(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)).
% 12.26/12.26  0 [] -class_Rings_Oring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),hAPP(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_Power_Opower__class_Opower(T_a,V_a,hAPP(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)).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_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_y_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_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_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_y_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_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,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_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  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).
% 12.26/12.26  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)))))).
% 12.26/12.26  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_x_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_y_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_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_x_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_y_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_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_x_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_y_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_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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)).
% 12.26/12.26  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_x_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_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_x_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_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_x_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_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  0 [] -class_Int_Onumber__ring(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,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(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))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Power_Opower__class_Opower(T_a,V_a,hAPP(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_k)),c_Groups_Ozero__class_Ozero(T_a))|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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,hAPP(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))).
% 12.26/12.26  0 [] -class_Rings_Oring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(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_Oone__class_Oone(T_a).
% 12.26/12.26  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)|hAPP(c_NthRoot_Osqrt,V_x)=V_y.
% 12.26/12.26  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,hAPP(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.
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))!=V_x_2|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=V_x_2| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2).
% 12.26/12.26  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,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,hAPP(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))))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y,hAPP(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))))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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,hAPP(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)))))),hAPP(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)))))))).
% 12.26/12.26  0 [] hAPP(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).
% 12.26/12.26  0 [] hAPP(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).
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(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))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(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)))))).
% 12.26/12.26  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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))))))).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x).
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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_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))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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_x_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_x_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 12.26/12.26  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_x_2,V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(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)).
% 12.26/12.26  0 [] c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z)=c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z)).
% 12.26/12.26  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_x_2,V_n_2))|V_n_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_x_2).
% 12.26/12.26  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_x_2,V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_x_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 12.26/12.26  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_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_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_x_2).
% 12.26/12.26  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_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n)=hAPP(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)).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a)=hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  0 [] -class_Groups_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n))=c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n).
% 12.26/12.26  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n).
% 12.26/12.26  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.
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.26/12.26  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_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.26/12.26  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_ma_2)!=c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)|V_ma_2=V_n_2.
% 12.26/12.26  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_ma_2)=c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)|V_ma_2!=V_n_2.
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  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))=hAPP(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)).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))=c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n).
% 12.26/12.26  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).
% 12.26/12.26  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))).
% 12.26/12.26  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),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))).
% 12.26/12.26  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).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Oring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)=hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)).
% 12.26/12.26  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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 12.26/12.26  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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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)).
% 12.26/12.26  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_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)).
% 12.26/12.26  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)).
% 12.26/12.26  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.
% 12.26/12.26  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)).
% 12.26/12.26  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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2).
% 12.26/12.26  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_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2).
% 12.26/12.26  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).
% 12.26/12.26  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)).
% 12.26/12.26  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.
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oarctan,V_x)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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)))))))))).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x)).
% 12.26/12.26  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,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)).
% 12.26/12.26  0 [] c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))).
% 12.26/12.26  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,hAPP(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)).
% 12.26/12.26  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,hAPP(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,hAPP(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,hAPP(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).
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n))=c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  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)|hAPP(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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(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)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(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)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(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)).
% 12.26/12.26  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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))=hAPP(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)).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)).
% 12.26/12.26  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 12.26/12.26  0 [] -class_Groups_Oabs__if(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 12.26/12.26  0 [] -class_Groups_Oabs__if(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 12.26/12.26  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)).
% 12.26/12.26  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).
% 12.26/12.26  0 [] c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)).
% 12.26/12.26  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,hAPP(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)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_d)).
% 12.26/12.26  0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 12.26/12.26  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 12.26/12.26  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 12.26/12.26  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 12.26/12.26  0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 12.26/12.26  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 12.26/12.26  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Osemiring__1(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 12.26/12.26  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 12.26/12.26  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 12.26/12.26  0 [] class_Int_Onumber__ring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Osemiring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Orderings_Oord(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ouminus(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oabs__if(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oring__1(tc_Int_Oint).
% 12.26/12.26  0 [] class_Power_Opower(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Ozero(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oring(tc_Int_Oint).
% 12.26/12.26  0 [] class_Rings_Oidom(tc_Int_Oint).
% 12.26/12.26  0 [] class_Int_Onumber(tc_Int_Oint).
% 12.26/12.26  0 [] class_Groups_Oone(tc_Int_Oint).
% 12.26/12.26  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Osemiring__1(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Power_Opower(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Int_Onumber(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Groups_Oone(tc_Nat_Onat).
% 12.26/12.26  0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 12.26/12.26  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 12.26/12.26  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 12.26/12.26  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 12.26/12.26  0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 12.26/12.26  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__field(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Fields_Olinordered__field(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Int_Onumber__ring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ouminus(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Osgn__if(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oabs__if(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Fields_Ofield(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Power_Opower(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_SEQ_Obanach(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Int_Onumber(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 12.26/12.26  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Osemiring__1(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Osemiring(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ouminus(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Oring__1(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Fields_Ofield(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Ozero(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_SEQ_Obanach(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Oring(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Rings_Oidom(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Int_Onumber(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Oone(tc_Complex_Ocomplex).
% 12.26/12.26  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Ozero__ne_q__one(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Power_Opower(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Int_Onumber(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] class_Groups_Oone(tc_Code__Numeral_Ocode__numeral).
% 12.26/12.26  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e).
% 12.26/12.26  end_of_list.
% 12.26/12.26  
% 12.26/12.26  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 12.26/12.26  
% 12.26/12.26  This ia a non-Horn set with equality.  The strategy will be
% 12.26/12.26  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 12.26/12.26  deletion, with positive clauses in sos and nonpositive
% 12.26/12.26  clauses in usable.
% 12.26/12.26  
% 12.26/12.26     dependent: set(knuth_bendix).
% 12.26/12.26     dependent: set(anl_eq).
% 12.26/12.26     dependent: set(para_from).
% 12.26/12.26     dependent: set(para_into).
% 12.26/12.26     dependent: clear(para_from_right).
% 12.26/12.26     dependent: clear(para_into_right).
% 12.26/12.26     dependent: set(para_from_vars).
% 12.26/12.26     dependent: set(eq_units_both_ways).
% 12.26/12.26     dependent: set(dynamic_demod_all).
% 12.26/12.26     dependent: set(dynamic_demod).
% 12.26/12.26     dependent: set(order_eq).
% 12.26/12.26     dependent: set(back_demod).
% 12.26/12.26     dependent: set(lrpo).
% 12.26/12.26     dependent: set(hyper_res).
% 12.26/12.26     dependent: set(unit_deletion).
% 12.26/12.26     dependent: set(factor).
% 12.26/12.26  
% 12.26/12.26  ------------> process usable:
% 12.26/12.26  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 12.26/12.26  ** KEPT (pick-wt=9): 2 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=B.
% 12.26/12.26    Following clause subsumed by 2 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=B.
% 12.26/12.26  ** KEPT (pick-wt=13): 3 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)=hAPP(c_Groups_Otimes__class_Otimes(A,C),B).
% 12.26/12.26  ** KEPT (pick-wt=17): 4 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,B),C))=hAPP(c_Groups_Otimes__class_Otimes(A,B),C).
% 12.26/12.26  ** KEPT (pick-wt=21): 5 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D))=hAPP(c_Groups_Otimes__class_Otimes(A,C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.26/12.26  ** KEPT (pick-wt=5): 6 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.26/12.26  ** KEPT (pick-wt=10): 7 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oone__class_Oone(A))=B.
% 12.26/12.26  ** KEPT (pick-wt=10): 8 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A)),B)=B.
% 12.26/12.26  ** KEPT (pick-wt=11): 9 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=11): 10 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=18): 11 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)!=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)|B=C.
% 12.26/12.26  ** KEPT (pick-wt=18): 12 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)|B!=C.
% 12.26/12.26  ** KEPT (pick-wt=18): 13 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)!=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)|B=C.
% 12.26/12.26  ** KEPT (pick-wt=18): 14 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A)=hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A)|B!=C.
% 12.26/12.26  ** KEPT (pick-wt=21): 15 [] -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)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C)).
% 12.26/12.26  ** KEPT (pick-wt=19): 16 [] -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),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B)).
% 12.26/12.26  ** KEPT (pick-wt=21): 17 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 12.26/12.26  ** KEPT (pick-wt=21): 18 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 12.26/12.26  ** KEPT (pick-wt=29): 19 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))=hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.26    Following clause subsumed by 5 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))=hAPP(c_Groups_Otimes__class_Otimes(A,D),hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),E)).
% 12.26/12.26  ** KEPT (pick-wt=29): 20 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))=hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))).
% 12.26/12.26  ** KEPT (pick-wt=21): 21 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D)=hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),C).
% 12.26/12.26  ** KEPT (pick-wt=21): 22 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D)=hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.26/12.26    Following clause subsumed by 22 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D)=hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.26/12.26  ** KEPT (pick-wt=30): 23 [] -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_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)).
% 12.26/12.26  ** KEPT (pick-wt=30): 24 [] -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_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,C),B))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,D,C),c_Rings_Oinverse__class_Odivide(A,D,B)).
% 12.26/12.26  ** KEPT (pick-wt=22): 25 [] -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_Rings_Oinverse__class_Odivide(A,C,B),D)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C).
% 12.26/12.26  ** KEPT (pick-wt=22): 26 [] -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_Rings_Oinverse__class_Odivide(A,C,B),D)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C).
% 12.26/12.26  ** KEPT (pick-wt=22): 27 [] -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_Rings_Oinverse__class_Odivide(A,D,B))|c_Orderings_Oord__class_Oless(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)).
% 12.26/12.26  ** KEPT (pick-wt=22): 28 [] -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_Rings_Oinverse__class_Odivide(A,D,B))| -c_Orderings_Oord__class_Oless(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)).
% 12.26/12.26  ** KEPT (pick-wt=22): 29 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D)|c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)).
% 12.26/12.26  ** KEPT (pick-wt=22): 30 [] -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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D).
% 12.26/12.26  ** KEPT (pick-wt=22): 31 [] -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_Rings_Oinverse__class_Odivide(A,C,B),D)|c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.26/12.26    Following clause subsumed by 30 during input processing: 0 [] -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_Rings_Oinverse__class_Odivide(A,C,B),D)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.26/12.26  ** KEPT (pick-wt=22): 32 [] -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_Rings_Oinverse__class_Odivide(A,D,B))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D).
% 12.26/12.26    Following clause subsumed by 29 during input processing: 0 [] -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_Rings_Oinverse__class_Odivide(A,D,B))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D).
% 12.26/12.26  ** KEPT (pick-wt=22): 33 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.26  ** KEPT (pick-wt=27): 34 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B).
% 12.26/12.26  ** KEPT (pick-wt=24): 35 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.26  ** KEPT (pick-wt=24): 36 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.26  ** KEPT (pick-wt=27): 37 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=27): 38 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.26  ** KEPT (pick-wt=22): 39 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 12.26/12.26  ** KEPT (pick-wt=27): 40 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|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),D).
% 12.26/12.26  ** KEPT (pick-wt=30): 41 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=30): 42 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.26  ** KEPT (pick-wt=22): 43 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C).
% 12.26/12.26  ** KEPT (pick-wt=27): 44 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.26/12.26  ** KEPT (pick-wt=24): 45 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=24): 46 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=27): 47 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=27): 48 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=22): 49 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.26  ** KEPT (pick-wt=27): 50 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=30): 51 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=30): 52 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=26): 53 [] -class_Fields_Ofield__inverse__zero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Odivide(A,B,C)),c_Rings_Oinverse__class_Odivide(A,D,E))=c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.26  ** KEPT (pick-wt=21): 54 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=21): 55 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 56 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 57 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 58 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 59 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 60 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 61 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=20): 62 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 63 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=20): 64 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 65 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=20): 66 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 67 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 68 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 69 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=20): 70 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=20): 71 [] -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)).
% 12.26/12.26  ** KEPT (pick-wt=30): 72 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,D,B)!=c_Rings_Oinverse__class_Odivide(A,E,C)|hAPP(c_Groups_Otimes__class_Otimes(A,D),C)=hAPP(c_Groups_Otimes__class_Otimes(A,E),B).
% 12.26/12.26  ** KEPT (pick-wt=30): 73 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,D,B)=c_Rings_Oinverse__class_Odivide(A,E,C)|hAPP(c_Groups_Otimes__class_Otimes(A,D),C)!=hAPP(c_Groups_Otimes__class_Otimes(A,E),B).
% 12.26/12.26  ** KEPT (pick-wt=23): 74 [] -class_Fields_Ofield__inverse__zero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))=c_Rings_Oinverse__class_Odivide(A,C,D).
% 12.26/12.26  ** KEPT (pick-wt=23): 75 [] -class_Fields_Ofield__inverse__zero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),B))=c_Rings_Oinverse__class_Odivide(A,C,D).
% 12.26/12.26  ** KEPT (pick-wt=19): 76 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,C)!=D|C=c_Groups_Ozero__class_Ozero(A)|B=hAPP(c_Groups_Otimes__class_Otimes(A,D),C).
% 12.26/12.26  ** KEPT (pick-wt=16): 77 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,C)!=D|C!=c_Groups_Ozero__class_Ozero(A)|D=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=16): 78 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=D|C!=c_Groups_Ozero__class_Ozero(A)|D!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=19): 79 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=D|B!=hAPP(c_Groups_Otimes__class_Otimes(A,D),C)|C=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=19): 80 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=D|B!=hAPP(c_Groups_Otimes__class_Otimes(A,D),C)|D!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=19): 81 [] -class_Fields_Ofield__inverse__zero(A)|B!=c_Rings_Oinverse__class_Odivide(A,C,D)|D=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),D)=C.
% 12.26/12.26  ** KEPT (pick-wt=16): 82 [] -class_Fields_Ofield__inverse__zero(A)|B!=c_Rings_Oinverse__class_Odivide(A,C,D)|D!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=16): 83 [] -class_Fields_Ofield__inverse__zero(A)|B=c_Rings_Oinverse__class_Odivide(A,C,D)|D!=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=19): 84 [] -class_Fields_Ofield__inverse__zero(A)|B=c_Rings_Oinverse__class_Odivide(A,C,D)|hAPP(c_Groups_Otimes__class_Otimes(A,B),D)!=C|D=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=19): 85 [] -class_Fields_Ofield__inverse__zero(A)|B=c_Rings_Oinverse__class_Odivide(A,C,D)|hAPP(c_Groups_Otimes__class_Otimes(A,B),D)!=C|B!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=13): 86 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A))|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.26/12.26  ** KEPT (pick-wt=16): 87 [] -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.
% 12.26/12.26  ** KEPT (pick-wt=16): 88 [] -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.
% 12.26/12.26  ** KEPT (pick-wt=13): 89 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=13): 90 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=13): 91 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=19): 92 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,C),B)!=D|C=c_Rings_Oinverse__class_Odivide(A,D,B).
% 12.26/12.26  ** KEPT (pick-wt=19): 93 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=hAPP(c_Groups_Otimes__class_Otimes(A,D),B)|c_Rings_Oinverse__class_Odivide(A,C,B)=D.
% 12.26/12.26  ** KEPT (pick-wt=19): 94 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,C,B)!=D|C=hAPP(c_Groups_Otimes__class_Otimes(A,D),B).
% 12.26/12.26    Following clause subsumed by 93 during input processing: 0 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,C,B)=D|C!=hAPP(c_Groups_Otimes__class_Otimes(A,D),B).
% 12.26/12.26  ** KEPT (pick-wt=19): 95 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=c_Rings_Oinverse__class_Odivide(A,D,B)|hAPP(c_Groups_Otimes__class_Otimes(A,C),B)=D.
% 12.26/12.26    Following clause subsumed by 92 during input processing: 0 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Rings_Oinverse__class_Odivide(A,D,B)|hAPP(c_Groups_Otimes__class_Otimes(A,C),B)!=D.
% 12.26/12.26  ** KEPT (pick-wt=21): 96 [] -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_Groups_Oone__class_Oone(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.26  ** KEPT (pick-wt=8): 97 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 12.26/12.26  ** KEPT (pick-wt=8): 98 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=13): 99 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.26/12.26  ** KEPT (pick-wt=18): 100 [] -class_Rings_Ono__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26    Following clause subsumed by 100 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=18): 101 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=14): 102 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=14): 103 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=11): 104 [] -class_Rings_Omult__zero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=11): 105 [] -class_Rings_Omult__zero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=7): 107 [copy,106,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 12.26/12.26    Following clause subsumed by 107 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 12.26/12.26  ** KEPT (pick-wt=10): 108 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=10): 109 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=19): 110 [] -class_Rings_Odivision__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))=c_Rings_Oinverse__class_Odivide(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D).
% 12.26/12.26  ** KEPT (pick-wt=9): 111 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Oone__class_Oone(A))=B.
% 12.26/12.26  ** KEPT (pick-wt=23): 112 [] -class_Rings_Olinordered__ring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.26/12.26  ** KEPT (pick-wt=23): 113 [] -class_Rings_Olinordered__ring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.26/12.26  ** KEPT (pick-wt=23): 114 [] -class_Rings_Olinordered__comm__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.26  ** KEPT (pick-wt=23): 115 [] -class_Rings_Olinordered__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.26  ** KEPT (pick-wt=23): 116 [] -class_Rings_Olinordered__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.26/12.26  ** KEPT (pick-wt=21): 117 [] -class_Rings_Olinordered__ring__strict(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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.26  ** KEPT (pick-wt=21): 118 [] -class_Rings_Olinordered__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=23): 119 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless(A,D,C).
% 12.26/12.26    Following clause subsumed by 112 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 12.26/12.26  ** KEPT (pick-wt=21): 120 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C))| -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),B).
% 12.26/12.26  ** KEPT (pick-wt=21): 121 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.26/12.26    Following clause subsumed by 118 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=21): 122 [] -class_Rings_Olinordered__semiring__strict(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=21): 123 [] -class_Rings_Olinordered__semiring__strict(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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.26  ** KEPT (pick-wt=23): 124 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless(A,C,D).
% 12.26/12.26  ** KEPT (pick-wt=23): 125 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 12.26/12.26  ** KEPT (pick-wt=24): 126 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|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)).
% 12.26/12.26  ** KEPT (pick-wt=23): 127 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.26/12.26  ** KEPT (pick-wt=23): 128 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=22): 129 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.26/12.26    Following clause subsumed by 125 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D).
% 12.26/12.26    Following clause subsumed by 112 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C).
% 12.26/12.26  ** KEPT (pick-wt=24): 130 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),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)).
% 12.26/12.26  ** KEPT (pick-wt=23): 131 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B).
% 12.26/12.26  ** KEPT (pick-wt=23): 132 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=22): 133 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B).
% 12.26/12.26  ** KEPT (pick-wt=23): 134 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 12.26/12.26    Following clause subsumed by 113 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B).
% 12.26/12.26  ** KEPT (pick-wt=11): 135 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=10): 136 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=10): 137 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oone__class_Oone(A))=B.
% 12.26/12.26  ** KEPT (pick-wt=10): 138 [] -class_Groups_Omonoid__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oone__class_Oone(A))=B.
% 12.26/12.26  ** KEPT (pick-wt=10): 139 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A)),B)=B.
% 12.26/12.26  ** KEPT (pick-wt=10): 140 [] -class_Groups_Omonoid__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A)),B)=B.
% 12.26/12.26  ** KEPT (pick-wt=11): 141 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26    Following clause subsumed by 141 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=11): 142 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26    Following clause subsumed by 142 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.26  ** KEPT (pick-wt=12): 143 [] -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).
% 12.26/12.26  ** KEPT (pick-wt=11): 144 [] -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.
% 12.26/12.26  ** KEPT (pick-wt=8): 145 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.26/12.26  ** KEPT (pick-wt=7): 146 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 12.26/12.26  ** KEPT (pick-wt=11): 147 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B.
% 12.26/12.26    Following clause subsumed by 147 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 12.26/12.26    Following clause subsumed by 145 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.26/12.26  ** KEPT (pick-wt=7): 148 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B.
% 12.26/12.26  ** KEPT (pick-wt=21): 149 [] -class_Rings_Oordered__cancel__semiring(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))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=21): 150 [] -class_Rings_Oordered__cancel__semiring(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)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.26  ** KEPT (pick-wt=21): 151 [] -class_Rings_Oordered__ring(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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.26  ** KEPT (pick-wt=21): 152 [] -class_Rings_Oordered__ring(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_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.26  ** KEPT (pick-wt=32): 153 [] -class_Rings_Oordered__semiring(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_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.26  ** KEPT (pick-wt=32): 154 [] -class_Rings_Oordered__semiring(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_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__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.26  ** KEPT (pick-wt=23): 155 [] -class_Rings_Oordered__ring(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.26/12.26  ** KEPT (pick-wt=23): 156 [] -class_Rings_Oordered__ring(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,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.26/12.27  ** KEPT (pick-wt=23): 157 [] -class_Rings_Oordered__comm__semiring(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.27  ** KEPT (pick-wt=23): 158 [] -class_Rings_Oordered__semiring(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,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.27  ** KEPT (pick-wt=23): 159 [] -class_Rings_Oordered__semiring(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,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.26/12.27    Following clause subsumed by 152 during input processing: 0 [] -class_Rings_Oordered__ring(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_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.27    Following clause subsumed by 150 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(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)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27    Following clause subsumed by 150 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(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))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27    Following clause subsumed by 149 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(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))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=21): 160 [] -class_Rings_Oordered__cancel__semiring(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),hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.26/12.27  ** KEPT (pick-wt=21): 161 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 162 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.26/12.27  ** KEPT (pick-wt=21): 163 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 164 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.26/12.27  ** KEPT (pick-wt=21): 165 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 166 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.26/12.27  ** KEPT (pick-wt=21): 167 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 168 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 169 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 170 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 171 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.26/12.27  ** KEPT (pick-wt=21): 172 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(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)).
% 12.26/12.27  ** KEPT (pick-wt=11): 173 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),B)).
% 12.26/12.27  ** KEPT (pick-wt=8): 174 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=8): 175 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 176 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=21): 177 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 178 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 179 [] -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).
% 12.26/12.27  ** KEPT (pick-wt=20): 180 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 181 [] -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).
% 12.26/12.27  ** KEPT (pick-wt=20): 182 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 183 [] -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).
% 12.26/12.27  ** KEPT (pick-wt=20): 184 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 185 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 186 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 187 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 188 [] -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).
% 12.26/12.27  ** KEPT (pick-wt=20): 189 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=18): 190 [] -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).
% 12.26/12.27  ** KEPT (pick-wt=18): 191 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=18): 192 [] 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).
% 12.26/12.27  ** KEPT (pick-wt=18): 193 [] 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)).
% 12.26/12.27  ** KEPT (pick-wt=18): 194 [] 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).
% 12.26/12.27  ** KEPT (pick-wt=18): 195 [] 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)).
% 12.26/12.27  ** KEPT (pick-wt=23): 196 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 197 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 198 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.26/12.27  ** KEPT (pick-wt=23): 199 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.26/12.27  ** KEPT (pick-wt=32): 200 [] -class_Rings_Olinordered__semiring__strict(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_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.27  ** KEPT (pick-wt=32): 201 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -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(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.27  ** KEPT (pick-wt=32): 202 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -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),D)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.27  ** KEPT (pick-wt=32): 203 [] -class_Rings_Olinordered__semiring__strict(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_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(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E)).
% 12.26/12.27  ** KEPT (pick-wt=23): 204 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 205 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 206 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 207 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 208 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.26/12.27  ** KEPT (pick-wt=23): 209 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.26/12.27  ** KEPT (pick-wt=25): 210 [] -class_Rings_Olinordered__idom(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,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),B).
% 12.26/12.27  ** KEPT (pick-wt=25): 211 [] -class_Rings_Olinordered__idom(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,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),B).
% 12.26/12.27  ** KEPT (pick-wt=20): 212 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 213 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=30): 214 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=30): 215 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=30): 216 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 217 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=20): 218 [] -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)).
% 12.26/12.27  ** KEPT (pick-wt=10): 219 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.27  ** KEPT (pick-wt=10): 220 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.26/12.27  ** KEPT (pick-wt=21): 221 [] -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_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 12.26/12.27  ** KEPT (pick-wt=21): 222 [] -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_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 12.26/12.27  ** KEPT (pick-wt=21): 223 [] -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_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 12.26/12.27  ** KEPT (pick-wt=21): 224 [] -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_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 12.26/12.27  ** KEPT (pick-wt=21): 225 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)),D)=hAPP(c_Groups_Otimes__class_Otimes(A,B),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.26/12.27  ** KEPT (pick-wt=10): 226 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 12.26/12.27  ** KEPT (pick-wt=10): 227 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 12.26/12.27  ** KEPT (pick-wt=22): 228 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C).
% 12.26/12.27  ** KEPT (pick-wt=27): 229 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.26/12.27  ** KEPT (pick-wt=24): 230 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=24): 231 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=27): 232 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=27): 233 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=22): 234 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.26/12.27  ** KEPT (pick-wt=27): 235 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=30): 236 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=30): 237 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.26/12.27  ** KEPT (pick-wt=22): 238 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.26/12.27  ** KEPT (pick-wt=27): 239 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B).
% 12.38/12.27  ** KEPT (pick-wt=24): 240 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.27  ** KEPT (pick-wt=24): 241 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.27  ** KEPT (pick-wt=27): 242 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=27): 243 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.27  ** KEPT (pick-wt=22): 244 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 12.38/12.27  ** KEPT (pick-wt=27): 245 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|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),D).
% 12.38/12.27  ** KEPT (pick-wt=30): 246 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=30): 247 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.27  ** KEPT (pick-wt=22): 248 [] -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,C,c_Rings_Oinverse__class_Odivide(A,D,B))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D).
% 12.38/12.27  ** KEPT (pick-wt=22): 249 [] -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,C,c_Rings_Oinverse__class_Odivide(A,D,B))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D).
% 12.38/12.27  ** KEPT (pick-wt=22): 250 [] -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,c_Rings_Oinverse__class_Odivide(A,C,B),D)|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.38/12.27  ** KEPT (pick-wt=22): 251 [] -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,c_Rings_Oinverse__class_Odivide(A,C,B),D)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)).
% 12.38/12.27    Following clause subsumed by 251 during input processing: 0 [] -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,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,C,B),D).
% 12.38/12.27    Following clause subsumed by 249 during input processing: 0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)).
% 12.38/12.27  ** KEPT (pick-wt=22): 252 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Rings_Oinverse__class_Odivide(A,D,B))|c_Orderings_Oord__class_Oless__e_q(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)).
% 12.38/12.27  ** KEPT (pick-wt=22): 253 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Rings_Oinverse__class_Odivide(A,D,B))| -c_Orderings_Oord__class_Oless__e_q(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,C),B)).
% 12.38/12.27  ** KEPT (pick-wt=22): 254 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,C,B),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C).
% 12.38/12.27  ** KEPT (pick-wt=22): 255 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,C,B),D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),C).
% 12.38/12.27  ** KEPT (pick-wt=30): 256 [] -class_Fields_Olinordered__field(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(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,C),B))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,D,C),c_Rings_Oinverse__class_Odivide(A,D,B)).
% 12.38/12.27  ** KEPT (pick-wt=30): 257 [] -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(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Groups_Otimes__class_Otimes(A,B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)).
% 12.38/12.27  ** KEPT (pick-wt=6): 258 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 12.38/12.27  ** KEPT (pick-wt=10): 259 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=10): 260 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27    Following clause subsumed by 259 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).
% 12.38/12.27    Following clause subsumed by 260 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).
% 12.38/12.27    Following clause subsumed by 259 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).
% 12.38/12.27  ** KEPT (pick-wt=10): 261 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=9): 262 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.27  ** KEPT (pick-wt=13): 263 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.38/12.27  ** KEPT (pick-wt=10): 264 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=10): 265 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=14): 266 [] -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).
% 12.38/12.27    Following clause subsumed by 263 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.
% 12.38/12.27    Following clause subsumed by 261 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).
% 12.38/12.27  ** KEPT (pick-wt=9): 267 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.38/12.27    Following clause subsumed by 259 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).
% 12.38/12.27    Following clause subsumed by 259 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).
% 12.38/12.27  ** KEPT (pick-wt=16): 268 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=24): 269 [] -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))).
% 12.38/12.27  ** KEPT (pick-wt=10): 270 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27    Following clause subsumed by 267 during input processing: 0 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=9): 271 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=13): 272 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=9): 273 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.27    Following clause subsumed by 268 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)).
% 12.38/12.27    Following clause subsumed by 272 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.
% 12.38/12.27    Following clause subsumed by 267 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.
% 12.38/12.27  ** KEPT (pick-wt=13): 274 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 275 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 276 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 277 [] -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).
% 12.38/12.27    Following clause subsumed by 272 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.
% 12.38/12.27  ** KEPT (pick-wt=14): 278 [] -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).
% 12.38/12.27    Following clause subsumed by 272 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.
% 12.38/12.27  ** KEPT (pick-wt=14): 279 [] -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).
% 12.38/12.27    Following clause subsumed by 268 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)).
% 12.38/12.27    Following clause subsumed by 270 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).
% 12.38/12.27  ** KEPT (pick-wt=13): 280 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=10): 281 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=14): 282 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=14): 283 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 284 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 12.38/12.27  ** KEPT (pick-wt=13): 285 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.27  ** KEPT (pick-wt=13): 286 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 12.38/12.27  ** KEPT (pick-wt=13): 287 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.27  ** KEPT (pick-wt=10): 288 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27    Following clause subsumed by 281 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=9): 289 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 12.38/12.27    Following clause subsumed by 262 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.27    Following clause subsumed by 281 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27    Following clause subsumed by 281 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27    Following clause subsumed by 262 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.27    Following clause subsumed by 280 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).
% 12.38/12.27    Following clause subsumed by 280 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.
% 12.38/12.27  ** KEPT (pick-wt=13): 290 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 12.38/12.27    Following clause subsumed by 280 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).
% 12.38/12.27    Following clause subsumed by 280 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.
% 12.38/12.27  ** KEPT (pick-wt=10): 291 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=9): 292 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.27    Following clause subsumed by 280 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).
% 12.38/12.27    Following clause subsumed by 292 during input processing: 0 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=9): 293 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=6): 294 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 12.38/12.27  ** KEPT (pick-wt=14): 295 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=14): 296 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=14): 297 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=14): 298 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 299 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.27    Following clause subsumed by 263 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).
% 12.38/12.27    Following clause subsumed by 263 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.
% 12.38/12.27  ** KEPT (pick-wt=13): 300 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.38/12.27    Following clause subsumed by 292 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.
% 12.38/12.27    Following clause subsumed by 264 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).
% 12.38/12.27    Following clause subsumed by 260 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).
% 12.38/12.27    Following clause subsumed by 299 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27    Following clause subsumed by 263 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).
% 12.38/12.27    Following clause subsumed by 300 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.38/12.27  ** KEPT (pick-wt=13): 301 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.38/12.27  ** KEPT (pick-wt=14): 302 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),$f3(B,C,A))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=14): 303 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,$f3(B,C,A),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=17): 304 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,$f3(B,C,A)),C),B)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=42): 305 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,E),B),hAPP(c_Groups_Otimes__class_Otimes(A,F),D)),C).
% 12.38/12.27  ** KEPT (pick-wt=42): 306 [] -class_Rings_Olinordered__semiring__1(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,E),B),hAPP(c_Groups_Otimes__class_Otimes(A,F),D)),C).
% 12.38/12.27  ** KEPT (pick-wt=14): 307 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=14): 308 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oone__class_Oone(A)).
% 12.38/12.27  ** KEPT (pick-wt=19): 309 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oone__class_Oone(A)).
% 12.38/12.27  ** KEPT (pick-wt=19): 310 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.27  ** KEPT (pick-wt=14): 311 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=14): 312 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.27  ** KEPT (pick-wt=19): 313 [] -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_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.27  ** KEPT (pick-wt=13): 314 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=13): 315 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27    Following clause subsumed by 315 during input processing: 0 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A).
% 12.38/12.27  ** KEPT (pick-wt=14): 316 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=14): 317 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=20): 318 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=9): 319 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 12.38/12.27  ** KEPT (pick-wt=11): 320 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,B).
% 12.38/12.27  ** KEPT (pick-wt=12): 321 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 12.38/12.27  ** KEPT (pick-wt=12): 322 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Oinverse(A,C)|B!=C.
% 12.38/12.27    Following clause subsumed by 321 during input processing: 0 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 12.38/12.27  ** KEPT (pick-wt=11): 323 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=17): 324 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=17): 326 [copy,325,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)).
% 12.38/12.27    Following clause subsumed by 326 during input processing: 0 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=17): 327 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=23): 328 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=17): 329 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=14): 330 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 12.38/12.27  ** KEPT (pick-wt=14): 331 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 12.38/12.27  ** KEPT (pick-wt=14): 332 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 12.38/12.27  ** KEPT (pick-wt=14): 333 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 12.38/12.27    Following clause subsumed by 330 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.
% 12.38/12.27  ** KEPT (pick-wt=14): 334 [] -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.
% 12.38/12.27    Following clause subsumed by 332 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.
% 12.38/12.27  ** KEPT (pick-wt=35): 336 [copy,335,flip.4] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,B))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 12.38/12.27  ** KEPT (pick-wt=35): 338 [copy,337,flip.4] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oplus__class_Oplus(A,B,C))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 12.38/12.27  ** KEPT (pick-wt=9): 339 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=20): 340 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|B=C.
% 12.38/12.27  ** KEPT (pick-wt=12): 341 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=13): 342 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 12.38/12.27    Following clause subsumed by 341 during input processing: 0 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 343 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 344 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=9): 345 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=19): 347 [copy,346,flip.2] -class_Fields_Ofield__inverse__zero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))=c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.27  ** KEPT (pick-wt=12): 348 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 349 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 12.38/12.27  ** KEPT (pick-wt=9): 350 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 12.38/12.27  ** KEPT (pick-wt=13): 351 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=9): 352 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.38/12.27  ** KEPT (pick-wt=9): 353 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.38/12.27  ** KEPT (pick-wt=13): 354 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=13): 355 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=9): 356 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.38/12.27  ** KEPT (pick-wt=9): 357 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.38/12.27  ** KEPT (pick-wt=12): 359 [copy,358,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).
% 12.38/12.27  ** KEPT (pick-wt=12): 361 [copy,360,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).
% 12.38/12.27  ** KEPT (pick-wt=9): 362 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.38/12.27  ** KEPT (pick-wt=9): 363 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.38/12.27  ** KEPT (pick-wt=16): 364 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 365 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=20): 366 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=16): 367 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=16): 368 [] -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)).
% 12.38/12.27    Following clause subsumed by 364 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).
% 12.38/12.27  ** KEPT (pick-wt=16): 369 [] -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).
% 12.38/12.27    Following clause subsumed by 365 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).
% 12.38/12.27  ** KEPT (pick-wt=16): 370 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 371 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 372 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 373 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 374 [] -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).
% 12.38/12.27  ** KEPT (pick-wt=16): 375 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=16): 376 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=20): 377 [] -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)).
% 12.38/12.27    Following clause subsumed by 371 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).
% 12.38/12.27    Following clause subsumed by 373 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).
% 12.38/12.27  ** KEPT (pick-wt=23): 378 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.38/12.27    Following clause subsumed by 378 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.38/12.27  ** KEPT (pick-wt=23): 379 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27    Following clause subsumed by 379 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27  ** KEPT (pick-wt=23): 380 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,B),D)).
% 12.38/12.27  ** KEPT (pick-wt=33): 381 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27  ** KEPT (pick-wt=30): 382 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),E))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27  ** KEPT (pick-wt=30): 383 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),B),hAPP(c_Groups_Otimes__class_Otimes(A,E),C))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,E),B)).
% 12.38/12.27  ** KEPT (pick-wt=23): 384 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27    Following clause subsumed by 384 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D)),C)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),C)).
% 12.38/12.27    Following clause subsumed by 381 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|B=D|C=E.
% 12.38/12.27    Following clause subsumed by 382 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|B!=D.
% 12.38/12.27    Following clause subsumed by 383 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),hAPP(c_Groups_Otimes__class_Otimes(A,D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),E),hAPP(c_Groups_Otimes__class_Otimes(A,D),C))|C!=E.
% 12.38/12.27  ** KEPT (pick-wt=23): 385 [] -class_Rings_Ocomm__semiring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),hAPP(c_Groups_Otimes__class_Otimes(A,C),D)).
% 12.38/12.27  ** KEPT (pick-wt=29): 387 [copy,386,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),D),E)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),D),E)).
% 12.38/12.27  ** KEPT (pick-wt=20): 388 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=20): 389 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=14): 390 [] -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)).
% 12.38/12.27  ** KEPT (pick-wt=12): 391 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 392 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=9): 393 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=9): 394 [] -class_Groups_Osgn__if(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 395 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=12): 396 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.27  ** KEPT (pick-wt=19): 398 [copy,397,flip.2] -class_RealVector_Oreal__normed__div__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.27  ** KEPT (pick-wt=19): 400 [copy,399,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.27  ** KEPT (pick-wt=9): 401 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 12.38/12.27  ** KEPT (pick-wt=14): 402 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=14): 403 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=14): 404 [] -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_Oinverse(A,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=14): 405 [] -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_Oinverse(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=19): 406 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=19): 407 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.27  ** KEPT (pick-wt=18): 408 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=19): 409 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.27  ** KEPT (pick-wt=19): 410 [] -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),B)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.27  ** KEPT (pick-wt=14): 411 [] -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_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=18): 412 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=14): 413 [] -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_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.27  ** KEPT (pick-wt=14): 414 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=14): 415 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.27  ** KEPT (pick-wt=14): 416 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=14): 417 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.27  ** KEPT (pick-wt=27): 418 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C))=hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.27  ** KEPT (pick-wt=15): 419 [] -class_Rings_Odivision__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),C)!=c_Groups_Oone__class_Oone(A)|c_Rings_Oinverse__class_Oinverse(A,B)=C.
% 12.38/12.27  ** KEPT (pick-wt=14): 421 [copy,420,flip.2] -class_Fields_Ofield(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,C))=c_Rings_Oinverse__class_Odivide(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=14): 423 [copy,422,flip.2] -class_Rings_Odivision__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,C))=c_Rings_Oinverse__class_Odivide(A,B,C).
% 12.38/12.27  ** KEPT (pick-wt=11): 424 [] -class_Fields_Ofield(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.27  ** KEPT (pick-wt=11): 425 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.27  ** KEPT (pick-wt=20): 426 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=18): 427 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=18): 428 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=23): 429 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=23): 430 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=27): 431 [] -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).
% 12.38/12.28    Following clause subsumed by 428 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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 432 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 433 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 434 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=15): 435 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=20): 436 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=20): 437 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 438 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 439 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 440 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=15): 441 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=18): 442 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=20): 443 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=20): 444 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=29): 445 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),E))!=c_Groups_Oplus__class_Oplus(A,D,hAPP(c_Groups_Otimes__class_Otimes(A,B),F)).
% 12.38/12.28  ** KEPT (pick-wt=10): 446 [] -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))).
% 12.38/12.28  ** KEPT (pick-wt=20): 448 [copy,447,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),C).
% 12.38/12.28  ** KEPT (pick-wt=20): 450 [copy,449,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.28  ** KEPT (pick-wt=17): 452 [copy,451,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))),B)=c_Groups_Oplus__class_Oplus(A,B,B).
% 12.38/12.28  ** KEPT (pick-wt=19): 453 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.28  ** KEPT (pick-wt=19): 454 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.28  ** KEPT (pick-wt=23): 455 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),A),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),B))=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).
% 12.38/12.28  ** KEPT (pick-wt=14): 456 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28  ** KEPT (pick-wt=14): 457 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28  ** KEPT (pick-wt=14): 458 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.28  ** KEPT (pick-wt=14): 459 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.28  ** KEPT (pick-wt=19): 460 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.28  ** KEPT (pick-wt=19): 461 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.28  ** KEPT (pick-wt=19): 462 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -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_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.28  ** KEPT (pick-wt=19): 463 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.28  ** KEPT (pick-wt=19): 464 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(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_Oone__class_Oone(A),B).
% 12.38/12.28  ** KEPT (pick-wt=14): 465 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28  ** KEPT (pick-wt=14): 466 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.28  ** KEPT (pick-wt=19): 467 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.28  ** KEPT (pick-wt=14): 468 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.28  ** KEPT (pick-wt=14): 469 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)).
% 12.38/12.28  ** KEPT (pick-wt=19): 470 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)).
% 12.38/12.28  ** KEPT (pick-wt=16): 471 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),B)=c_Groups_Oone__class_Oone(A).
% 12.38/12.28  ** KEPT (pick-wt=16): 472 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Rings_Oinverse__class_Oinverse(A,B)),B)=c_Groups_Oone__class_Oone(A).
% 12.38/12.28  ** KEPT (pick-wt=16): 473 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Rings_Oinverse__class_Oinverse(A,B))=c_Groups_Oone__class_Oone(A).
% 12.38/12.28    Following clause subsumed by 425 during input processing: 0 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B).
% 12.38/12.28  ** KEPT (pick-wt=20): 474 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=20): 475 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=18): 476 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=18): 477 [] -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)).
% 12.38/12.28    Following clause subsumed by 476 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)).
% 12.38/12.28    Following clause subsumed by 477 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)).
% 12.38/12.28  ** KEPT (pick-wt=12): 478 [] -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))).
% 12.38/12.28  ** KEPT (pick-wt=40): 480 [copy,479,flip.4] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),C),hAPP(c_Groups_Otimes__class_Otimes(A,E),B)),hAPP(c_Groups_Otimes__class_Otimes(A,B),C))=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)).
% 12.38/12.28  ** KEPT (pick-wt=25): 482 [copy,481,flip.3] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),D)),B)=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D).
% 12.38/12.28  ** KEPT (pick-wt=25): 484 [copy,483,flip.3] -class_Fields_Ofield__inverse__zero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)),B)=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D).
% 12.38/12.28  ** KEPT (pick-wt=25): 486 [copy,485,flip.3] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C),D),B)=c_Groups_Oplus__class_Oplus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)).
% 12.38/12.28  ** KEPT (pick-wt=25): 488 [copy,487,flip.3] -class_Fields_Ofield__inverse__zero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,D),B)),B)=c_Groups_Oplus__class_Oplus(A,D,c_Rings_Oinverse__class_Odivide(A,C,B)).
% 12.38/12.28  ** KEPT (pick-wt=21): 489 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=21): 490 [] -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)))).
% 12.38/12.28  ** KEPT (pick-wt=11): 491 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.28  ** KEPT (pick-wt=18): 492 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28  ** KEPT (pick-wt=26): 493 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=22): 494 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)))|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=22): 495 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)))|C=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=22): 496 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=22): 497 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A))|C=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=26): 498 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C)),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=18): 499 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))).
% 12.38/12.28  ** KEPT (pick-wt=38): 500 [] -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),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),D))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,C),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,D),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))).
% 12.38/12.28  ** KEPT (pick-wt=38): 501 [] -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),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,B),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),D))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),C),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),D)).
% 12.38/12.28  ** KEPT (pick-wt=21): 502 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=21): 503 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=25): 504 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B),hAPP(c_Groups_Otimes__class_Otimes(A,C),C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28  ** KEPT (pick-wt=15): 505 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=15): 506 [] -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)).
% 12.38/12.28  ** KEPT (pick-wt=13): 507 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=13): 508 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=14): 509 [] -class_Fields_Olinordered__field(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),$f4(B,C,A))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.28  ** KEPT (pick-wt=16): 510 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oplus__class_Oplus(A,C,$f4(C,B,A)))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.28  ** KEPT (pick-wt=15): 511 [] -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,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)),A).
% 12.38/12.28  ** KEPT (pick-wt=26): 512 [] -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),B)|hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,A),B))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),hAPP(c_Transcendental_Oln,B)).
% 12.38/12.28  ** KEPT (pick-wt=22): 513 [] -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),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),hAPP(c_Transcendental_Oln,B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.28  ** KEPT (pick-wt=22): 514 [] -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),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),hAPP(c_Transcendental_Oln,B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.28  ** KEPT (pick-wt=20): 515 [] -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),B)|hAPP(c_Transcendental_Oln,A)!=hAPP(c_Transcendental_Oln,B)|A=B.
% 12.38/12.28  ** KEPT (pick-wt=20): 516 [] -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),B)|hAPP(c_Transcendental_Oln,A)=hAPP(c_Transcendental_Oln,B)|A!=B.
% 12.38/12.28  ** KEPT (pick-wt=11): 517 [] -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,hAPP(c_Transcendental_Oln,A),A).
% 12.38/12.28  ** KEPT (pick-wt=22): 518 [] -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),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),hAPP(c_Transcendental_Oln,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.38/12.28  ** KEPT (pick-wt=22): 519 [] -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),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),hAPP(c_Transcendental_Oln,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.38/12.28  ** KEPT (pick-wt=12): 520 [] -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_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A)).
% 12.38/12.28  ** KEPT (pick-wt=17): 521 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))| -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_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28  ** KEPT (pick-wt=17): 522 [] -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,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.28  ** KEPT (pick-wt=17): 523 [] -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,hAPP(c_Transcendental_Oln,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.38/12.28    Following clause subsumed by 522 during input processing: 0 [] -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,hAPP(c_Transcendental_Oln,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.38/12.28  ** KEPT (pick-wt=15): 524 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_Transcendental_Oln,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.28  ** KEPT (pick-wt=15): 525 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_Transcendental_Oln,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.28    Following clause subsumed by 521 during input processing: 0 [] -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),hAPP(c_Transcendental_Oln,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28  ** KEPT (pick-wt=17): 526 [] -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),hAPP(c_Transcendental_Oln,A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28  ** KEPT (pick-wt=12): 527 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A)).
% 12.38/12.28  ** KEPT (pick-wt=17): 528 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))| -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_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28    Following clause subsumed by 528 during input processing: 0 [] -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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28    Following clause subsumed by 520 during input processing: 0 [] -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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.38/12.28    Following clause subsumed by 238 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))).
% 12.38/12.28    Following clause subsumed by 239 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B).
% 12.38/12.28    Following clause subsumed by 240 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 241 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 242 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 243 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 244 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)).
% 12.38/12.28    Following clause subsumed by 245 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 246 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 247 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 238 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)).
% 12.38/12.28    Following clause subsumed by 239 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B).
% 12.38/12.28    Following clause subsumed by 240 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 241 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 242 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 243 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 244 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 12.38/12.28    Following clause subsumed by 245 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))|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_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 246 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 247 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 228 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C).
% 12.38/12.28    Following clause subsumed by 229 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)).
% 12.38/12.28    Following clause subsumed by 230 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 231 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 232 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 233 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 234 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 235 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 236 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 237 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 228 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C).
% 12.38/12.28    Following clause subsumed by 229 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))).
% 12.38/12.28    Following clause subsumed by 230 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 231 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 232 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 233 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 234 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 235 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 236 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 237 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28  ** KEPT (pick-wt=14): 529 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)).
% 12.38/12.28  ** KEPT (pick-wt=23): 531 [copy,530,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)).
% 12.38/12.28  ** KEPT (pick-wt=17): 533 [copy,532,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)).
% 12.38/12.28    Following clause subsumed by 533 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)).
% 12.38/12.28  ** KEPT (pick-wt=16): 534 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=16): 535 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=14): 536 [] -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.
% 12.38/12.28  ** KEPT (pick-wt=14): 537 [] -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.
% 12.38/12.28  ** KEPT (pick-wt=12): 538 [] -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)!=C|C=c_Int_Onumber__class_Onumber__of(A,B).
% 12.38/12.28  ** KEPT (pick-wt=12): 539 [] -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)=C|C!=c_Int_Onumber__class_Onumber__of(A,B).
% 12.38/12.28  ** KEPT (pick-wt=27): 541 [copy,540,flip.2] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C))),D)=hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,C)),D)).
% 12.38/12.28  ** KEPT (pick-wt=19): 542 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,C))=c_Int_Onumber__class_Onumber__of(A,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)).
% 12.38/12.28    Following clause subsumed by 542 during input processing: 0 [flip.2] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,C))=c_Int_Onumber__class_Onumber__of(A,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,B),C)).
% 12.38/12.28  ** KEPT (pick-wt=16): 543 [] -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).
% 12.38/12.28  ** KEPT (pick-wt=16): 544 [] -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).
% 12.38/12.28    Following clause subsumed by 260 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)).
% 12.38/12.28    Following clause subsumed by 259 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)).
% 12.38/12.28  ** KEPT (pick-wt=31): 545 [] -class_Int_Onumber(A)| -class_Rings_Osemiring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Int_Onumber__class_Onumber__of(A,D))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),hAPP(c_Groups_Otimes__class_Otimes(A,C),c_Int_Onumber__class_Onumber__of(A,D))).
% 12.38/12.28  ** KEPT (pick-wt=31): 546 [] -class_Int_Onumber(A)| -class_Rings_Osemiring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),C),hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)).
% 12.38/12.28    Following clause subsumed by 81 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|B!=c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))|c_Int_Onumber__class_Onumber__of(A,D)=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))=C.
% 12.38/12.28    Following clause subsumed by 82 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|B!=c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))|c_Int_Onumber__class_Onumber__of(A,D)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 83 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|B=c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))|c_Int_Onumber__class_Onumber__of(A,D)!=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 84 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|B=c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))!=C|c_Int_Onumber__class_Onumber__of(A,D)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 85 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|B=c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D))|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))!=C|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 81 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Rings_Oinverse__class_Odivide(A,C,D)|D=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)=C.
% 12.38/12.28    Following clause subsumed by 82 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Rings_Oinverse__class_Odivide(A,C,D)|D!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 83 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Rings_Oinverse__class_Odivide(A,C,D)|D!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 84 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Rings_Oinverse__class_Odivide(A,C,D)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)!=C|D=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 85 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Rings_Oinverse__class_Odivide(A,C,D)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)!=C|c_Int_Onumber__class_Onumber__of(A,B)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 76 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,C)!=c_Int_Onumber__class_Onumber__of(A,D)|C=c_Groups_Ozero__class_Ozero(A)|B=hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C).
% 12.38/12.28    Following clause subsumed by 77 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,C)!=c_Int_Onumber__class_Onumber__of(A,D)|C!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(A,D)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 78 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=c_Int_Onumber__class_Onumber__of(A,D)|C!=c_Groups_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(A,D)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 79 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=c_Int_Onumber__class_Onumber__of(A,D)|B!=hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)|C=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 80 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,C)=c_Int_Onumber__class_Onumber__of(A,D)|B!=hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)|c_Int_Onumber__class_Onumber__of(A,D)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 76 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C))!=D|c_Int_Onumber__class_Onumber__of(A,C)=c_Groups_Ozero__class_Ozero(A)|B=hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)).
% 12.38/12.28    Following clause subsumed by 77 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C))!=D|c_Int_Onumber__class_Onumber__of(A,C)!=c_Groups_Ozero__class_Ozero(A)|D=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 78 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C))=D|c_Int_Onumber__class_Onumber__of(A,C)!=c_Groups_Ozero__class_Ozero(A)|D!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 79 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C))=D|B!=hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))|c_Int_Onumber__class_Onumber__of(A,C)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 80 during input processing: 0 [] -class_Fields_Ofield__inverse__zero(A)| -class_Int_Onumber(A)|c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C))=D|B!=hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))|D!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.28    Following clause subsumed by 425 during input processing: 0 [] -class_Int_Onumber(A)| -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,B))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,B)).
% 12.38/12.28    Following clause subsumed by 33 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C))).
% 12.38/12.28    Following clause subsumed by 34 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B).
% 12.38/12.28    Following clause subsumed by 35 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 36 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 37 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 38 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 39 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,C)).
% 12.38/12.28    Following clause subsumed by 40 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 41 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,C),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 42 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,c_Int_Onumber__class_Onumber__of(A,C)),D)| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,D),c_Int_Onumber__class_Onumber__of(A,C)),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 33 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C)).
% 12.38/12.28    Following clause subsumed by 34 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B).
% 12.38/12.28    Following clause subsumed by 35 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 36 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 37 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 38 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 39 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 12.38/12.28    Following clause subsumed by 40 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))|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_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 41 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 42 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,B,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,D)),C),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.28    Following clause subsumed by 43 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C).
% 12.38/12.28    Following clause subsumed by 44 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D)).
% 12.38/12.28    Following clause subsumed by 45 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 46 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 47 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 48 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 49 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D).
% 12.38/12.28    Following clause subsumed by 50 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)|c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 51 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 52 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Rings_Oinverse__class_Odivide(A,C,D))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),D))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,B),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 43 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C).
% 12.38/12.28    Following clause subsumed by 44 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D))).
% 12.38/12.28    Following clause subsumed by 45 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)| -c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 46 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 47 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 48 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D))| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.28    Following clause subsumed by 49 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(A,D)).
% 12.38/12.29    Following clause subsumed by 50 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)|c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29    Following clause subsumed by 51 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(A,D),c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29    Following clause subsumed by 52 during input processing: 0 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber(A)|c_Orderings_Oord__class_Oless(A,B,c_Rings_Oinverse__class_Odivide(A,C,c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)),C)| -c_Orderings_Oord__class_Oless(A,C,hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,D)))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=12): 547 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)).
% 12.38/12.29  ** KEPT (pick-wt=9): 548 [] -class_RealVector_Oreal__normed__field(A)|c_Deriv_Oderiv(A,c_Groups_Otimes__class_Otimes(A,B),C,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 549 [] -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)).
% 12.38/12.29  ** KEPT (pick-wt=10): 550 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.29    Following clause subsumed by 491 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.29    Following clause subsumed by 550 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.29    Following clause subsumed by 491 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.29  ** KEPT (pick-wt=16): 551 [] -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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 552 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B)).
% 12.38/12.29  ** KEPT (pick-wt=12): 553 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 554 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=21): 556 [copy,555,flip.2] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))),C)=hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B))),C).
% 12.38/12.29  ** KEPT (pick-wt=13): 557 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))=c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)).
% 12.38/12.29    Following clause subsumed by 557 during input processing: 0 [flip.2] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))=c_Groups_Ouminus__class_Ouminus(A,c_Int_Onumber__class_Onumber__of(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=12): 558 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 559 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=13): 561 [copy,560,flip.2] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=14): 562 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 563 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.38/12.29  ** KEPT (pick-wt=17): 564 [] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|hAPP(c_Transcendental_Oexp(A),c_Groups_Ouminus__class_Ouminus(A,B))=c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Transcendental_Oexp(A),B)).
% 12.38/12.29  ** KEPT (pick-wt=12): 565 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)!=hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B)|A=B.
% 12.38/12.29  ** KEPT (pick-wt=12): 566 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)=hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B)|A!=B.
% 12.38/12.29  ** KEPT (pick-wt=9): 567 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=12): 568 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)=B.
% 12.38/12.29  ** KEPT (pick-wt=12): 569 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)!=B.
% 12.38/12.29  ** KEPT (pick-wt=11): 571 [copy,570,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=11): 573 [copy,572,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=12): 574 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=12): 575 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29    Following clause subsumed by 571 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29    Following clause subsumed by 573 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=14): 576 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29    Following clause subsumed by 576 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=14): 577 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 12.38/12.29    Following clause subsumed by 577 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 578 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 579 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.29    Following clause subsumed by 579 during input processing: 0 [] -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_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=14): 580 [] -class_Lattices_Oboolean__algebra(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=14): 581 [] -class_Lattices_Oboolean__algebra(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.29    Following clause subsumed by 580 during input processing: 0 [] -class_Lattices_Oboolean__algebra(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 582 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 583 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 584 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 12.38/12.29    Following clause subsumed by 584 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 585 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29    Following clause subsumed by 585 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=21): 586 [] -class_Rings_Oidom(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)!=hAPP(c_Groups_Otimes__class_Otimes(A,C),C)|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 12.38/12.29  ** KEPT (pick-wt=16): 587 [] -class_Rings_Oidom(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=hAPP(c_Groups_Otimes__class_Otimes(A,C),C)|B!=C.
% 12.38/12.29  ** KEPT (pick-wt=18): 588 [] -class_Rings_Oidom(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=hAPP(c_Groups_Otimes__class_Otimes(A,C),C)|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 12.38/12.29  ** KEPT (pick-wt=17): 589 [] -class_Rings_Oring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))=hAPP(c_Groups_Otimes__class_Otimes(A,B),C).
% 12.38/12.29  ** KEPT (pick-wt=17): 590 [] -class_Rings_Oring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)=hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 12.38/12.29  ** KEPT (pick-wt=17): 592 [copy,591,flip.2] -class_Rings_Oring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29  ** KEPT (pick-wt=17): 594 [copy,593,flip.2] -class_Rings_Oring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29  ** KEPT (pick-wt=17): 595 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29    Following clause subsumed by 595 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29  ** KEPT (pick-wt=17): 596 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29    Following clause subsumed by 596 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),C)).
% 12.38/12.29  ** KEPT (pick-wt=13): 597 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C))=C.
% 12.38/12.29  ** KEPT (pick-wt=13): 598 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C))=C.
% 12.38/12.29  ** KEPT (pick-wt=17): 599 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=17): 600 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 12.38/12.29  ** KEPT (pick-wt=15): 601 [] -class_Rings_Odivision__ring(A)|c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 12.38/12.29  ** KEPT (pick-wt=15): 602 [] -class_Fields_Ofield__inverse__zero(A)|c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Ouminus__class_Ouminus(A,C)).
% 12.38/12.29  ** KEPT (pick-wt=15): 603 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Rings_Oinverse__class_Odivide(A,B,C).
% 12.38/12.29  ** KEPT (pick-wt=15): 605 [copy,604,flip.2] -class_RealVector_Oreal__normed__field(A)|c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,B,C))=c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 12.38/12.29  ** KEPT (pick-wt=13): 606 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=9): 607 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 12.38/12.29  ** KEPT (pick-wt=15): 608 [] -class_Groups_Ouminus(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A),C),D)=c_Groups_Ouminus__class_Ouminus(A,hAPP(C,D)).
% 12.38/12.29  ** KEPT (pick-wt=12): 609 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 12.38/12.29  ** KEPT (pick-wt=12): 610 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 12.38/12.29  ** KEPT (pick-wt=9): 611 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 12.38/12.29  ** KEPT (pick-wt=12): 612 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.38/12.29    Following clause subsumed by 612 during input processing: 0 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.38/12.29  ** KEPT (pick-wt=12): 613 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 12.38/12.29    Following clause subsumed by 613 during input processing: 0 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C|c_Groups_Ouminus__class_Ouminus(A,C)!=B.
% 12.38/12.29  ** KEPT (pick-wt=12): 614 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 12.38/12.29  ** KEPT (pick-wt=12): 615 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 12.38/12.29  ** KEPT (pick-wt=14): 616 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.29    Following clause subsumed by 552 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.29    Following clause subsumed by 616 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.29  ** KEPT (pick-wt=11): 617 [] -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.
% 12.38/12.29  ** KEPT (pick-wt=12): 618 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=21): 619 [] -c_Orderings_Oord__class_Oless(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(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),B)).
% 12.38/12.29  ** KEPT (pick-wt=17): 620 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=17): 621 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=21): 622 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=11): 623 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=15): 624 [] -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.
% 12.38/12.29  ** KEPT (pick-wt=12): 625 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=11): 626 [] 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.
% 12.38/12.29  ** KEPT (pick-wt=17): 627 [] -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)).
% 12.38/12.29  ** KEPT (pick-wt=17): 628 [] 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)).
% 12.38/12.29  ** KEPT (pick-wt=14): 629 [] -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)).
% 12.38/12.29  ** KEPT (pick-wt=10): 630 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=10): 631 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=12): 632 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 633 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=12): 634 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 635 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=14): 636 [] -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)).
% 12.38/12.29    Following clause subsumed by 635 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).
% 12.38/12.29  ** KEPT (pick-wt=18): 637 [] -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)).
% 12.38/12.29  ** KEPT (pick-wt=8): 638 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B).
% 12.38/12.29  ** KEPT (pick-wt=7): 639 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A!=B.
% 12.38/12.29  ** KEPT (pick-wt=11): 640 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|A=B.
% 12.38/12.29  ** KEPT (pick-wt=14): 641 [] -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)).
% 12.38/12.29  ** KEPT (pick-wt=11): 642 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)!=B|hAPP(c_Transcendental_Oln,B)=A.
% 12.38/12.29    Following clause subsumed by 642 during input processing: 0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)!=B|hAPP(c_Transcendental_Oln,B)=A.
% 12.38/12.29  ** KEPT (pick-wt=11): 643 [] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|hAPP(c_Transcendental_Oexp(A),B)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=13): 644 [] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|c_Deriv_Oderiv(A,c_Transcendental_Oexp(A),B,hAPP(c_Transcendental_Oexp(A),B)).
% 12.38/12.29  ** KEPT (pick-wt=13): 645 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=13): 646 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 647 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 648 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=13): 649 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=13): 650 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 651 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 652 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=13): 653 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=13): 654 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 655 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 656 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 657 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 658 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=13): 659 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=13): 660 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 661 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.38/12.29  ** KEPT (pick-wt=14): 662 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.38/12.29  ** KEPT (pick-wt=11): 663 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=14): 664 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=14): 665 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=11): 666 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=11): 667 [] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=14): 668 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C.
% 12.38/12.29  ** KEPT (pick-wt=14): 670 [copy,669,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.38/12.29  ** KEPT (pick-wt=20): 671 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A)|B=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 672 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 12.38/12.29  ** KEPT (pick-wt=16): 673 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.38/12.29  ** KEPT (pick-wt=19): 674 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Odivide(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B))=c_Rings_Oinverse__class_Odivide(A,C,B).
% 12.38/12.29  ** KEPT (pick-wt=19): 675 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Odivide(A,C,B))=c_Rings_Oinverse__class_Odivide(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=17): 676 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=12): 677 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 12.38/12.29  ** KEPT (pick-wt=12): 678 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 12.38/12.29  ** KEPT (pick-wt=12): 679 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=B.
% 12.38/12.29  ** KEPT (pick-wt=12): 680 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=B.
% 12.38/12.29  ** KEPT (pick-wt=8): 681 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=8): 682 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=11): 683 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.29  ** KEPT (pick-wt=11): 684 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.29  ** KEPT (pick-wt=12): 685 [] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|hAPP(c_Transcendental_Oexp(A),c_Groups_Ozero__class_Ozero(A))=c_Groups_Oone__class_Oone(A).
% 12.38/12.29  ** KEPT (pick-wt=23): 687 [copy,686,flip.3] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Transcendental_Oexp(A),B)),hAPP(c_Transcendental_Oexp(A),C))=hAPP(c_Transcendental_Oexp(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 12.38/12.29    Following clause subsumed by 687 during input processing: 0 [] -class_RealVector_Oreal__normed__field(A)| -class_SEQ_Obanach(A)|hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Transcendental_Oexp(A),B)),hAPP(c_Transcendental_Oexp(A),C))=hAPP(c_Transcendental_Oexp(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 12.38/12.29  ** KEPT (pick-wt=14): 688 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 689 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 690 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 691 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 692 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 693 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.38/12.29  ** KEPT (pick-wt=14): 694 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.38/12.29  ** KEPT (pick-wt=14): 695 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.38/12.29  ** KEPT (pick-wt=13): 696 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=13): 697 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=13): 698 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29  ** KEPT (pick-wt=13): 699 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29  ** KEPT (pick-wt=13): 700 [] -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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A)).
% 12.38/12.29  ** KEPT (pick-wt=13): 701 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=13): 702 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.29  ** KEPT (pick-wt=13): 703 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29    Following clause subsumed by 700 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29  ** KEPT (pick-wt=13): 704 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))=A.
% 12.38/12.29  ** KEPT (pick-wt=13): 705 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))!=A|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29    Following clause subsumed by 704 during input processing: 0 [] hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,A))=A| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.38/12.29  ** KEPT (pick-wt=15): 706 [] -class_RealVector_Oreal__normed__field(A)| -c_Deriv_Oderiv(A,B,C,D)| -c_Deriv_Oderiv(A,B,C,E)|D=E.
% 12.38/12.29  ** KEPT (pick-wt=15): 707 [] -class_RealVector_Oreal__normed__field(A)| -c_Deriv_Oderiv(A,B,C,D)|D!=E|c_Deriv_Oderiv(A,B,C,E).
% 12.38/12.29    Following clause subsumed by 707 during input processing: 0 [] -class_RealVector_Oreal__normed__field(A)| -c_Deriv_Oderiv(A,B,C,D)|D!=E|c_Deriv_Oderiv(A,B,C,E).
% 12.38/12.29  ** KEPT (pick-wt=12): 708 [] -class_Groups_Osgn__if(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=17): 709 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A).
% 12.38/12.29  ** KEPT (pick-wt=19): 710 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.38/12.29  ** KEPT (pick-wt=15): 711 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.38/12.29  ** KEPT (pick-wt=15): 712 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29    Following clause subsumed by 711 during input processing: 0 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=16): 713 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A))=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,A)).
% 12.38/12.29  ** KEPT (pick-wt=51): 714 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),E),F)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),E),F),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),F)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E,B).
% 12.38/12.29  ** KEPT (pick-wt=35): 715 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),D),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,E)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,B).
% 12.38/12.29  ** KEPT (pick-wt=51): 716 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),E),F)| -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,D),E),F))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,F,D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,E).
% 12.38/12.29  ** KEPT (pick-wt=35): 717 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),D),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,E,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B,D).
% 12.38/12.29  ** KEPT (pick-wt=10): 718 [] A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=15): 719 [] 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),A)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=5): 720 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.38/12.29  ** KEPT (pick-wt=25): 722 [copy,721,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C))!=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,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.38/12.29  ** KEPT (pick-wt=24): 724 [copy,723,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),C))!=A| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C).
% 12.38/12.29  ** KEPT (pick-wt=26): 725 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -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),B).
% 12.38/12.29  ** KEPT (pick-wt=27): 726 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B),C),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)| -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,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.29  ** KEPT (pick-wt=19): 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__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),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,A),B)).
% 12.38/12.29  ** 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__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)).
% 12.38/12.29  ** KEPT (pick-wt=19): 729 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Int_Onumber__class_Onumber__of(A,C)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C)))).
% 12.38/12.29  ** KEPT (pick-wt=19): 730 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Int_Onumber__class_Onumber__of(A,C)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,C)))).
% 12.38/12.29  ** KEPT (pick-wt=18): 731 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f5(C,B,A)).
% 12.38/12.29  ** KEPT (pick-wt=33): 732 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,D,$f5(C,B,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(A,B),hAPP(A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D))).
% 12.38/12.29  ** KEPT (pick-wt=18): 733 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f6(C,B,A)).
% 12.38/12.29  ** KEPT (pick-wt=33): 734 [] -c_Deriv_Oderiv(tc_RealDef_Oreal,A,B,C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,D,$f6(C,B,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)),hAPP(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=9): 735 [] -class_Rings_Osemiring__1(A)| -c_Int_Oiszero(A,B)|B=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=9): 736 [] -class_Rings_Osemiring__1(A)|c_Int_Oiszero(A,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.38/12.29  ** KEPT (pick-wt=6): 737 [] -class_Rings_Osemiring__1(A)|c_Int_Oiszero(A,c_Groups_Ozero__class_Ozero(A)).
% 12.38/12.29  ** KEPT (pick-wt=6): 738 [] -class_Rings_Osemiring__1(A)| -c_Int_Oiszero(A,c_Groups_Oone__class_Oone(A)).
% 12.38/12.29  ** KEPT (pick-wt=18): 739 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Groups_Ozero__class_Ozero(A)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))).
% 12.38/12.29  ** KEPT (pick-wt=18): 740 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Groups_Ozero__class_Ozero(A)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))).
% 12.38/12.29  ** KEPT (pick-wt=18): 741 [] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)!=c_Int_Onumber__class_Onumber__of(A,B)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))).
% 12.38/12.29  ** KEPT (pick-wt=18): 742 [] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,B)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))).
% 12.38/12.29  ** KEPT (pick-wt=16): 743 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_Opred(B))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(A,B)).
% 12.38/12.29  ** KEPT (pick-wt=16): 744 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 745 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=16): 746 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=11): 747 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=11): 748 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=10): 749 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=10): 750 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=10): 751 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=10): 752 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=16): 753 [] -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).
% 12.38/12.29  ** KEPT (pick-wt=12): 754 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=12): 755 [] 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).
% 12.38/12.29  ** KEPT (pick-wt=4): 756 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 12.38/12.29  ** KEPT (pick-wt=8): 757 [] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OPls).
% 12.41/12.29    Following clause subsumed by 757 during input processing: 0 [flip.2] -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OPls).
% 12.41/12.29  ** KEPT (pick-wt=10): 758 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,B,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls))=B.
% 12.41/12.29  ** KEPT (pick-wt=10): 759 [] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls),B)=B.
% 12.41/12.29  ** KEPT (pick-wt=5): 760 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.41/12.29  ** KEPT (pick-wt=16): 761 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=20): 762 [] 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).
% 12.41/12.29  ** KEPT (pick-wt=20): 763 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)),C))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.29  ** KEPT (pick-wt=16): 764 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Int_OPls)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.29  ** KEPT (pick-wt=7): 765 [] -class_Int_Onumber__ring(A)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OPls)).
% 12.41/12.29  ** KEPT (pick-wt=14): 766 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=14): 767 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=9): 768 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=9): 769 [] 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).
% 12.41/12.29  ** KEPT (pick-wt=13): 770 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 771 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 772 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 773 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 774 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 775 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 776 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 777 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=15): 778 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=19): 779 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)!=c_Groups_Oone__class_Oone(A)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))).
% 12.41/12.29  ** KEPT (pick-wt=19): 780 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,B)=c_Groups_Oone__class_Oone(A)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))).
% 12.41/12.29  ** KEPT (pick-wt=19): 781 [] -class_Int_Onumber__ring(A)|c_Groups_Oone__class_Oone(A)!=c_Int_Onumber__class_Onumber__of(A,B)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))).
% 12.41/12.29  ** KEPT (pick-wt=19): 782 [] -class_Int_Onumber__ring(A)|c_Groups_Oone__class_Oone(A)=c_Int_Onumber__class_Onumber__of(A,B)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))).
% 12.41/12.29  ** KEPT (pick-wt=4): 784 [copy,783,flip.1] c_Int_OBit1(A)!=c_Int_OPls.
% 12.41/12.29    Following clause subsumed by 784 during input processing: 0 [] c_Int_OBit1(A)!=c_Int_OPls.
% 12.41/12.29  ** KEPT (pick-wt=10): 785 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=10): 786 [] 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).
% 12.41/12.29    Following clause subsumed by 785 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).
% 12.41/12.29    Following clause subsumed by 786 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).
% 12.41/12.29  ** KEPT (pick-wt=10): 787 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=10): 788 [] 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).
% 12.41/12.29    Following clause subsumed by 787 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).
% 12.41/12.29    Following clause subsumed by 788 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).
% 12.41/12.29  ** KEPT (pick-wt=8): 789 [] c_Int_OBit1(A)!=c_Int_OBit1(B)|A=B.
% 12.41/12.29  ** KEPT (pick-wt=8): 790 [] c_Int_OBit1(A)=c_Int_OBit1(B)|A!=B.
% 12.41/12.29  ** KEPT (pick-wt=9): 791 [] -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).
% 12.41/12.29  ** KEPT (pick-wt=9): 792 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=11): 793 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 794 [] 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)).
% 12.41/12.30  ** KEPT (pick-wt=9): 795 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 796 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=10): 797 [] -class_Int_Onumber__ring(A)| -class_Int_Oring__char__0(A)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(B))).
% 12.41/12.30  ** KEPT (pick-wt=19): 798 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 799 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))),B)=B.
% 12.41/12.30  ** KEPT (pick-wt=12): 800 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)))=B.
% 12.41/12.30  ** KEPT (pick-wt=9): 801 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))=c_Groups_Oone__class_Oone(A).
% 12.41/12.30  ** KEPT (pick-wt=9): 802 [] -class_Int_Onumber__ring(A)|c_Groups_Oone__class_Oone(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)).
% 12.41/12.30  ** KEPT (pick-wt=13): 803 [] -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.
% 12.41/12.30    Following clause subsumed by 803 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.
% 12.41/12.30  ** KEPT (pick-wt=15): 804 [] -class_Fields_Ofield(A)| -class_Int_Onumber__ring(A)|c_Rings_Oinverse__class_Oinverse(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)))=c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls)).
% 12.41/12.30  ** KEPT (pick-wt=9): 805 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 806 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=9): 807 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 808 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=8): 809 [] -class_Int_Onumber__ring(A)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit1(c_Int_OPls))).
% 12.41/12.30  ** KEPT (pick-wt=16): 810 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=16): 811 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=16): 812 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=16): 813 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=16): 814 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=16): 815 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=16): 816 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=16): 817 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=17): 818 [] -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))).
% 12.41/12.30  ** KEPT (pick-wt=17): 819 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=5): 820 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.41/12.30  ** KEPT (pick-wt=21): 821 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))| -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,B,C).
% 12.41/12.30  ** KEPT (pick-wt=16): 822 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 12.41/12.30  ** KEPT (pick-wt=4): 823 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.41/12.30  ** KEPT (pick-wt=7): 824 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.41/12.30  ** KEPT (pick-wt=7): 825 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 12.41/12.30    Following clause subsumed by 823 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.41/12.30    Following clause subsumed by 825 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 12.41/12.30    Following clause subsumed by 824 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.41/12.30  ** KEPT (pick-wt=12): 826 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 12.41/12.30  ** KEPT (pick-wt=12): 827 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 12.41/12.30  ** KEPT (pick-wt=12): 828 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 12.41/12.30  ** KEPT (pick-wt=12): 829 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 12.41/12.30  ** KEPT (pick-wt=11): 830 [] -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.
% 12.41/12.30  ** KEPT (pick-wt=12): 831 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=7): 832 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.41/12.30    Following clause subsumed by 820 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.41/12.30    Following clause subsumed by 825 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).
% 12.41/12.30    Following clause subsumed by 820 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.41/12.30  ** KEPT (pick-wt=8): 833 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=10): 834 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=11): 835 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=11): 836 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=15): 837 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=9): 838 [] -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).
% 12.41/12.30    Following clause subsumed by 832 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).
% 12.41/12.30  ** KEPT (pick-wt=18): 839 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=14): 840 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)|A!=C.
% 12.41/12.30  ** KEPT (pick-wt=15): 841 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=18): 842 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=14): 843 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|B!=C.
% 12.41/12.30  ** KEPT (pick-wt=15): 844 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=16): 845 [] hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.41/12.30  ** KEPT (pick-wt=12): 846 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=12): 847 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=11): 848 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=17): 849 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=18): 850 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=14): 851 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 852 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 853 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=14): 854 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=14): 855 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=7): 856 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 12.41/12.30  ** KEPT (pick-wt=7): 857 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 12.41/12.30  ** KEPT (pick-wt=8): 858 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.41/12.30    Following clause subsumed by 832 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.41/12.30  ** KEPT (pick-wt=11): 859 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.41/12.30    Following clause subsumed by 858 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).
% 12.41/12.30    Following clause subsumed by 859 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.
% 12.41/12.30    Following clause subsumed by 858 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).
% 12.41/12.30    Following clause subsumed by 832 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 12.41/12.30    Following clause subsumed by 858 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).
% 12.41/12.30    Following clause subsumed by 824 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.41/12.30    Following clause subsumed by 859 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)|A=B.
% 12.41/12.30  ** KEPT (pick-wt=12): 861 [copy,860,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.
% 12.41/12.30  ** KEPT (pick-wt=10): 862 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 12.41/12.30  ** KEPT (pick-wt=14): 863 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=14): 864 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=11): 865 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 866 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=14): 867 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=18): 868 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 869 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=11): 870 [] -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).
% 12.41/12.30    Following clause subsumed by 870 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).
% 12.41/12.30    Following clause subsumed by 869 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).
% 12.41/12.30  ** KEPT (pick-wt=16): 871 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)).
% 12.41/12.30    Following clause subsumed by 822 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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)).
% 12.41/12.30  ** KEPT (pick-wt=20): 872 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),D)).
% 12.41/12.30  ** KEPT (pick-wt=12): 873 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=12): 874 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=16): 875 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=12): 876 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=12): 877 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=16): 878 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=18): 879 [] -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).
% 12.41/12.30    Following clause subsumed by 853 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).
% 12.41/12.30    Following clause subsumed by 852 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).
% 12.41/12.30  ** KEPT (pick-wt=14): 880 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.41/12.30  ** KEPT (pick-wt=14): 881 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 12.41/12.30  ** KEPT (pick-wt=19): 882 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(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).
% 12.41/12.30  ** KEPT (pick-wt=17): 883 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.41/12.30  ** KEPT (pick-wt=16): 884 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.41/12.30  ** KEPT (pick-wt=21): 885 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))| -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,B,C).
% 12.41/12.30  ** KEPT (pick-wt=17): 886 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 12.41/12.30  ** KEPT (pick-wt=16): 887 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 12.41/12.30  ** KEPT (pick-wt=21): 888 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B))| -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,A,C).
% 12.41/12.30    Following clause subsumed by 888 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B),C)).
% 12.41/12.30    Following clause subsumed by 885 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B)).
% 12.41/12.30  ** KEPT (pick-wt=15): 890 [copy,889,flip.1] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30  ** KEPT (pick-wt=21): 891 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 12.41/12.30    Following clause subsumed by 871 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 12.41/12.30    Following clause subsumed by 821 during input processing: 0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 12.41/12.30    Following clause subsumed by 822 during input processing: 0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 12.41/12.30  ** KEPT (pick-wt=19): 892 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|B=C.
% 12.41/12.30    Following clause subsumed by 843 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|B!=C.
% 12.41/12.30    Following clause subsumed by 884 during input processing: 0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.41/12.30    Following clause subsumed by 885 during input processing: 0 [] -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,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.41/12.30    Following clause subsumed by 842 during input processing: 0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)!=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 12.41/12.30    Following clause subsumed by 844 during input processing: 0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.41/12.30    Following clause subsumed by 843 during input processing: 0 [] hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),B)=hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A),C)|B!=C.
% 12.41/12.30    Following clause subsumed by 866 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)).
% 12.41/12.30    Following clause subsumed by 865 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)).
% 12.41/12.30    Following clause subsumed by 852 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)).
% 12.41/12.30    Following clause subsumed by 853 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)).
% 12.41/12.30    Following clause subsumed by 858 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).
% 12.41/12.30  ** KEPT (pick-wt=12): 894 [copy,893,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f8(B,A))=B.
% 12.41/12.30    Following clause subsumed by 862 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 12.41/12.30  ** KEPT (pick-wt=17): 895 [] -class_Fields_Olinordered__field__inverse__zero(A)| -class_Int_Onumber__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.41/12.30  ** KEPT (pick-wt=32): 896 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hBOOL(hAPP(B,$f9(C,B,A)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A)))).
% 12.41/12.30  ** KEPT (pick-wt=35): 897 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -hBOOL(hAPP(B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,$f9(C,B,A),A)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,C),A)))).
% 12.41/12.30  ** KEPT (pick-wt=15): 898 [] -class_Int_Onumber__ring(A)| -class_Int_Oring__char__0(A)| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B)))|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,B)).
% 12.41/12.30  ** KEPT (pick-wt=15): 899 [] -class_Int_Onumber__ring(A)| -class_Int_Oring__char__0(A)|c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B)))| -c_Int_Oiszero(A,c_Int_Onumber__class_Onumber__of(A,B)).
% 12.41/12.30  ** KEPT (pick-wt=10): 900 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 901 [] 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).
% 12.41/12.30    Following clause subsumed by 900 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).
% 12.41/12.30    Following clause subsumed by 901 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).
% 12.41/12.30  ** KEPT (pick-wt=10): 902 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 903 [] 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).
% 12.41/12.30    Following clause subsumed by 902 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).
% 12.41/12.30    Following clause subsumed by 903 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).
% 12.41/12.30  ** KEPT (pick-wt=5): 904 [] c_Int_OBit1(A)!=c_Int_OBit0(B).
% 12.41/12.30  ** KEPT (pick-wt=5): 905 [] c_Int_OBit0(A)!=c_Int_OBit1(B).
% 12.41/12.30  ** KEPT (pick-wt=8): 906 [] c_Int_OBit0(A)!=c_Int_OBit0(B)|A=B.
% 12.41/12.30  ** KEPT (pick-wt=8): 907 [] c_Int_OBit0(A)=c_Int_OBit0(B)|A!=B.
% 12.41/12.30  ** KEPT (pick-wt=7): 908 [] c_Int_OBit0(A)!=c_Int_OPls|A=c_Int_OPls.
% 12.41/12.30  ** KEPT (pick-wt=7): 909 [] c_Int_OBit0(A)=c_Int_OPls|A!=c_Int_OPls.
% 12.41/12.30  ** KEPT (pick-wt=7): 911 [copy,910,flip.1] c_Int_OBit0(A)!=c_Int_OPls|c_Int_OPls=A.
% 12.41/12.30  ** KEPT (pick-wt=7): 913 [copy,912,flip.1] c_Int_OBit0(A)=c_Int_OPls|c_Int_OPls!=A.
% 12.41/12.30  ** KEPT (pick-wt=9): 914 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 915 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=9): 916 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 917 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=11): 918 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=11): 919 [] 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)).
% 12.41/12.30  ** KEPT (pick-wt=10): 920 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 921 [] 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).
% 12.41/12.30    Following clause subsumed by 920 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).
% 12.41/12.30    Following clause subsumed by 921 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).
% 12.41/12.30  ** KEPT (pick-wt=9): 922 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 923 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=9): 924 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=9): 925 [] 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).
% 12.41/12.30  ** KEPT (pick-wt=10): 926 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 927 [] 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).
% 12.41/12.30    Following clause subsumed by 926 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).
% 12.41/12.30    Following clause subsumed by 927 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).
% 12.41/12.30  ** KEPT (pick-wt=19): 928 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=10): 929 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 930 [] 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).
% 12.41/12.30    Following clause subsumed by 929 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).
% 12.41/12.30    Following clause subsumed by 930 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).
% 12.41/12.30  ** KEPT (pick-wt=10): 931 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=10): 932 [] 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).
% 12.41/12.30    Following clause subsumed by 931 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).
% 12.41/12.30    Following clause subsumed by 932 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).
% 12.41/12.30  ** KEPT (pick-wt=19): 933 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(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,B))=c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(B)).
% 12.41/12.30  ** KEPT (pick-wt=15): 934 [] -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))).
% 12.41/12.30  ** KEPT (pick-wt=15): 935 [] -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))).
% 12.41/12.30  ** KEPT (pick-wt=28): 936 [] A!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C))|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A)=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C).
% 12.41/12.30  ** KEPT (pick-wt=28): 937 [] A=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C))|hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A)!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C).
% 12.41/12.30  ** KEPT (pick-wt=16): 938 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(A,B,B).
% 12.41/12.30  ** KEPT (pick-wt=16): 939 [] -class_Int_Onumber__ring(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)=c_Groups_Oplus__class_Oplus(A,B,B).
% 12.41/12.30  ** KEPT (pick-wt=14): 940 [] -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))).
% 12.41/12.30  ** KEPT (pick-wt=18): 941 [] -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))))).
% 12.41/12.30  ** KEPT (pick-wt=18): 942 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=21): 943 [] -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))))).
% 12.41/12.30  ** KEPT (pick-wt=21): 944 [] -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).
% 12.41/12.30    Following clause subsumed by 943 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).
% 12.41/12.30  ** KEPT (pick-wt=21): 945 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=30): 946 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|B!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,A,B).
% 12.41/12.30  ** KEPT (pick-wt=28): 947 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,A,B).
% 12.41/12.30  ** KEPT (pick-wt=39): 948 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|B!=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,A,B).
% 12.41/12.30  ** KEPT (pick-wt=41): 949 [] A=B| -c_Deriv_Oderiv(tc_RealDef_Oreal,C,$f10(D,C,B,A),D)|hAPP(C,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)))))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(C,A),hAPP(C,B)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.41/12.30  ** KEPT (pick-wt=12): 950 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 951 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 952 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 953 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 954 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 955 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 956 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 957 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30    Following clause subsumed by 955 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),hAPP(c_NthRoot_Osqrt,A)).
% 12.41/12.30  ** KEPT (pick-wt=10): 958 [] hAPP(c_NthRoot_Osqrt,A)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=10): 959 [] hAPP(c_NthRoot_Osqrt,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=12): 960 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B)).
% 12.41/12.30  ** KEPT (pick-wt=12): 961 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.41/12.30    Following clause subsumed by 960 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.41/12.30  ** KEPT (pick-wt=12): 962 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B)).
% 12.41/12.30  ** KEPT (pick-wt=12): 963 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.41/12.30    Following clause subsumed by 962 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),hAPP(c_NthRoot_Osqrt,B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.41/12.30  ** KEPT (pick-wt=10): 964 [] hAPP(c_NthRoot_Osqrt,A)!=hAPP(c_NthRoot_Osqrt,B)|A=B.
% 12.41/12.30  ** KEPT (pick-wt=10): 965 [] hAPP(c_NthRoot_Osqrt,A)=hAPP(c_NthRoot_Osqrt,B)|A!=B.
% 12.41/12.30  ** KEPT (pick-wt=12): 966 [] -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),hAPP(c_NthRoot_Osqrt,A)).
% 12.41/12.30  ** KEPT (pick-wt=11): 967 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_NthRoot_Osqrt,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=12): 968 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 969 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 970 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.41/12.30    Following clause subsumed by 966 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 971 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 972 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).
% 12.41/12.30  ** KEPT (pick-wt=12): 973 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30  ** KEPT (pick-wt=12): 974 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)).
% 12.41/12.30    Following clause subsumed by 972 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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,A)).
% 12.41/12.30  ** KEPT (pick-wt=15): 975 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|hAPP(c_NthRoot_Osqrt,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=10): 976 [] hAPP(c_NthRoot_Osqrt,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=10): 977 [] hAPP(c_NthRoot_Osqrt,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.41/12.30  ** KEPT (pick-wt=17): 979 [copy,978,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),A).
% 12.41/12.30  ** KEPT (pick-wt=18): 980 [] -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,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),A).
% 12.41/12.30  ** KEPT (pick-wt=21): 981 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.41/12.30  ** KEPT (pick-wt=60): 982 [] -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,hAPP(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).
% 12.41/12.30  ** KEPT (pick-wt=10): 983 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=21): 984 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,D))=c_Power_Opower__class_Opower(A,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 12.41/12.30  ** KEPT (pick-wt=18): 985 [] -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,c_Power_Opower__class_Opower(A,B,C),D)=c_Power_Opower__class_Opower(A,B,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C),D)).
% 12.41/12.30  ** KEPT (pick-wt=22): 987 [copy,986,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,D,C))=c_Power_Opower__class_Opower(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),D),C).
% 12.41/12.30  ** KEPT (pick-wt=9): 988 [] -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,B,c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 12.41/12.30  ** KEPT (pick-wt=21): 989 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=23): 990 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=27): 991 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=20): 992 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=20): 993 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=20): 994 [] -class_Groups_Omonoid__mult(A)|c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,B),B)),B).
% 12.41/12.30  ** KEPT (pick-wt=14): 995 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=17): 996 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=17): 997 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=16): 998 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Groups_Otimes__class_Otimes(A,B),B)=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)))).
% 12.41/12.30  ** KEPT (pick-wt=16): 999 [] -class_Groups_Omonoid__mult(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))))=hAPP(c_Groups_Otimes__class_Otimes(A,B),B).
% 12.41/12.30  ** KEPT (pick-wt=14): 1000 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=21): 1001 [] -class_Rings_Oring__1(A)|c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(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)))).
% 12.41/12.30  ** KEPT (pick-wt=26): 1002 [] -class_Groups_Omonoid__mult(A)|c_Power_Opower__class_Opower(A,B,hAPP(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)))),C))=c_Power_Opower__class_Opower(A,c_Power_Opower__class_Opower(A,B,C),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.41/12.30  ** KEPT (pick-wt=14): 1003 [] -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))))).
% 12.41/12.30  ** KEPT (pick-wt=29): 1004 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=32): 1005 [] -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.
% 12.41/12.30  ** KEPT (pick-wt=18): 1006 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=18): 1007 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=14): 1008 [] -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)).
% 12.41/12.30  ** KEPT (pick-wt=27): 1009 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=27): 1010 [] -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).
% 12.41/12.30  ** KEPT (pick-wt=31): 1011 [] -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).
% 12.41/12.30    Following clause subsumed by 999 during input processing: 0 [] -class_Groups_Omonoid__mult(A)| -class_Int_Onumber(A)|c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B)),c_Int_Onumber__class_Onumber__of(A,B)).
% 12.41/12.30  ** KEPT (pick-wt=23): 1012 [] -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_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A)|B=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.41/12.30  ** KEPT (pick-wt=17): 1013 [] -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_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 12.41/12.30  ** KEPT (pick-wt=19): 1014 [] -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_Oone__class_Oone(A)|B!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.41/12.30  ** KEPT (pick-wt=26): 1015 [] -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,B,hAPP(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)))),C))=hAPP(c_Groups_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,C)),c_Power_Opower__class_Opower(A,B,C)).
% 12.41/12.31  ** KEPT (pick-wt=29): 1016 [] -class_Rings_Oring__1(A)|c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,B),hAPP(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)))),C))=c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)).
% 12.41/12.31  ** KEPT (pick-wt=25): 1017 [] 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).
% 12.41/12.31  ** KEPT (pick-wt=25): 1018 [] 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).
% 12.41/12.31  ** KEPT (pick-wt=29): 1019 [] 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).
% 12.41/12.31  ** KEPT (pick-wt=29): 1020 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=24): 1021 [] -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)))))).
% 12.41/12.31  ** KEPT (pick-wt=28): 1022 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=28): 1023 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=32): 1024 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=24): 1025 [] -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)).
% 12.41/12.31  ** KEPT (pick-wt=32): 1026 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=28): 1027 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=28): 1028 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=47): 1030 [copy,1029,flip.2] -class_Int_Onumber__ring(A)|c_Groups_Oplus__class_Oplus(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))))),hAPP(c_Groups_Otimes__class_Otimes(A,hAPP(c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)),C))=c_Power_Opower__class_Opower(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 12.41/12.31  ** KEPT (pick-wt=22): 1031 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Power_Opower__class_Opower(A,B,hAPP(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)))),C)),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 12.41/12.31  ** KEPT (pick-wt=18): 1032 [] -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,hAPP(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)))),C))).
% 12.41/12.31  ** KEPT (pick-wt=20): 1033 [] -class_Rings_Oring__1(A)|c_Power_Opower__class_Opower(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)),hAPP(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)))),B))=c_Groups_Oone__class_Oone(A).
% 12.41/12.31  ** KEPT (pick-wt=20): 1034 [] 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)|hAPP(c_NthRoot_Osqrt,B)=A.
% 12.41/12.31  ** KEPT (pick-wt=17): 1035 [] -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,hAPP(c_NthRoot_Osqrt,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=A.
% 12.41/12.31  ** KEPT (pick-wt=17): 1036 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c
% 12.41/12.31  Search stopped in tp_alloc by max_mem option.
% 12.41/12.31  _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).
% 12.41/12.31    Following clause subsumed by 1035 during input processing: 0 [] c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(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).
% 12.41/12.31  ** KEPT (pick-wt=19): 1037 [] -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,hAPP(c_NthRoot_Osqrt,A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 12.41/12.31  ** KEPT (pick-wt=26): 1038 [] hAPP(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).
% 12.41/12.31  ** KEPT (pick-wt=26): 1039 [] hAPP(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).
% 12.41/12.31  ** KEPT (pick-wt=21): 1040 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,A)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A).
% 12.41/12.31  ** KEPT (pick-wt=26): 1041 [] -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)).
% 12.41/12.31  ** KEPT (pick-wt=19): 1042 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=17): 1043 [] -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).
% 12.41/12.31  ** KEPT (pick-wt=13): 1044 [] 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).
% 12.41/12.31  ** KEPT (pick-wt=12): 1045 [] 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).
% 12.41/12.31  
% 12.41/12.31  Search stopped in tp_alloc by max_mem option.
% 12.41/12.31  
% 12.41/12.31  ============ end of search ============
% 12.41/12.31  
% 12.41/12.31  -------------- statistics -------------
% 12.41/12.31  clauses given                  0
% 12.41/12.31  clauses generated              0
% 12.41/12.31  clauses kept                1002
% 12.41/12.31  clauses forward subsumed     276
% 12.41/12.31  clauses back subsumed          0
% 12.41/12.31  Kbytes malloced            11718
% 12.41/12.31  
% 12.41/12.31  ----------- times (seconds) -----------
% 12.41/12.31  user CPU time          0.12          (0 hr, 0 min, 0 sec)
% 12.41/12.31  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 12.41/12.31  wall-clock time       12             (0 hr, 0 min, 12 sec)
% 12.41/12.31  
% 12.41/12.31  Process 11308 finished Wed Jul 27 03:05:02 2022
% 12.41/12.31  Otter interrupted
% 12.41/12.31  PROOF NOT FOUND
%------------------------------------------------------------------------------