TSTP Solution File: SWW238+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n019.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  : 600s
% DateTime : Thu Jul 21 01:15:56 EDT 2022

% Result   : Timeout 300.10s 300.37s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW238+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun  4 12:16:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.47/1.80  ============================== Prover9 ===============================
% 1.47/1.80  Prover9 (32) version 2009-11A, November 2009.
% 1.47/1.80  Process 5598 was started by sandbox on n019.cluster.edu,
% 1.47/1.80  Sat Jun  4 12:16:41 2022
% 1.47/1.80  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5444_n019.cluster.edu".
% 1.47/1.80  ============================== end of head ===========================
% 1.47/1.80  
% 1.47/1.80  ============================== INPUT =================================
% 1.47/1.80  
% 1.47/1.80  % Reading from file /tmp/Prover9_5444_n019.cluster.edu
% 1.47/1.80  
% 1.47/1.80  set(prolog_style_variables).
% 1.47/1.80  set(auto2).
% 1.47/1.80      % set(auto2) -> set(auto).
% 1.47/1.80      % set(auto) -> set(auto_inference).
% 1.47/1.80      % set(auto) -> set(auto_setup).
% 1.47/1.80      % set(auto_setup) -> set(predicate_elim).
% 1.47/1.80      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.47/1.80      % set(auto) -> set(auto_limits).
% 1.47/1.80      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.47/1.80      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.47/1.80      % set(auto) -> set(auto_denials).
% 1.47/1.80      % set(auto) -> set(auto_process).
% 1.47/1.80      % set(auto2) -> assign(new_constants, 1).
% 1.47/1.80      % set(auto2) -> assign(fold_denial_max, 3).
% 1.47/1.80      % set(auto2) -> assign(max_weight, "200.000").
% 1.47/1.80      % set(auto2) -> assign(max_hours, 1).
% 1.47/1.80      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.47/1.80      % set(auto2) -> assign(max_seconds, 0).
% 1.47/1.80      % set(auto2) -> assign(max_minutes, 5).
% 1.47/1.80      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.47/1.80      % set(auto2) -> set(sort_initial_sos).
% 1.47/1.80      % set(auto2) -> assign(sos_limit, -1).
% 1.47/1.80      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.47/1.80      % set(auto2) -> assign(max_megs, 400).
% 1.47/1.80      % set(auto2) -> assign(stats, some).
% 1.47/1.80      % set(auto2) -> clear(echo_input).
% 1.47/1.80      % set(auto2) -> set(quiet).
% 1.47/1.80      % set(auto2) -> clear(print_initial_clauses).
% 1.47/1.80      % set(auto2) -> clear(print_given).
% 1.47/1.80  assign(lrs_ticks,-1).
% 1.47/1.80  assign(sos_limit,10000).
% 1.47/1.80  assign(order,kbo).
% 1.47/1.80  set(lex_order_vars).
% 1.47/1.80  clear(print_given).
% 1.47/1.80  
% 1.47/1.80  % formulas(sos).  % not echoed (1272 formulas)
% 1.47/1.80  
% 1.47/1.80  ============================== end of input ==========================
% 1.47/1.80  
% 1.47/1.80  % From the command line: assign(max_seconds, 300).
% 1.47/1.80  
% 1.47/1.80  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.47/1.80  
% 1.47/1.80  % Formulas that are not ordinary clauses:
% 1.47/1.80  1 (all V_g_2 all V_f_2 ((all B_x hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)) -> V_f_2 = V_g_2)) # label(fact_ext) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.80  2 (all V_z all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) # label(fact_complex__mod__triangle__sub) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.80  3 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))))) # label(fact_norm__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.80  4 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))))) # label(fact_norm__mult__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.80  5 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x))) # label(fact_order__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.80  6 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_real__add__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  7 (all V_y all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) # label(fact_norm__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  8 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Oadd__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  9 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  10 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Oadd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  11 (all V_db_2 all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_ab_2 != V_b_2 & V_ca_2 != V_db_2 <-> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  12 (all V_ma all V_mazh all V_mzh (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_mzh,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_mazh,V_ma)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_da____),V_ma),V_mzh) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,V_mazh)))) # label(fact_ath) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  13 (all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_norm__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  14 (all V_r c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)) # label(fact_real__norm__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  15 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)) # label(fact_real__mult__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  16 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__eq__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  17 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))) # label(fact_real__mult__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  18 (all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a))) # label(fact_abs__norm__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  19 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__right_Ozero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  20 (all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  21 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  22 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__left_Ozero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  23 (all V_b all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult_Ozero__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  24 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  25 (all V_ab_2 all V_b_2 all 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_ab_2) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  26 (all V_a all 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)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  27 (all V_a all 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)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  28 (all V_w all V_z2 all V_z1 hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))) # label(fact_real__add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  29 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_norm__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  30 (all V_d all V_c all V_b all V_a all V_r all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  31 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  32 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funE) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  33 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  34 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  35 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z))))) # label(fact_order__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  36 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  37 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  38 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_b = V_c -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  39 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  40 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  41 (all V_x_2 all V_y_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  42 (all V_x_2 all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) -> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))))) # label(fact_le__funD) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  43 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  44 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (V_x_2 = V_y_2 <-> c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  45 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x))) # label(fact_linorder__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  46 (all V_g_2 all V_f_2 all T_a all T_b (class_Orderings_Oord(T_b) -> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) <-> (all B_x c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  47 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  48 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  49 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  50 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  51 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  52 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  53 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  54 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  55 (all V_d all V_c all V_b all V_a all 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  56 (all V_c all V_b all V_a all 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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  57 (all V_c all V_b all V_a all 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  58 (all V_d all V_c all V_a all 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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  59 (all V_d all V_c all V_a all 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)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  60 (all V_c all V_a all 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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  61 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) -> V_z = V_w))) # label(fact_real__le__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  62 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)))) # label(fact_real__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  63 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z))) # label(fact_real__le__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  64 (all V_w c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w)) # label(fact_real__le__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  65 (all V_za_2 all V_x_2 all V_y_2 all V_w_2 all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) <-> V_w_2 = V_x_2 | V_y_2 = V_za_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  66 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  67 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Oadd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  68 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Oadd__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  69 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  70 (all V_y all V_x all V_c all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y))) -> V_x = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_norm__ratiotest__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  71 (all V_b all V_a all T_a (class_Rings_Oordered__ring__abs(T_a) -> ((c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))) & (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(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))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  72 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))))) # label(fact_abs__mult__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  73 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(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)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  74 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  75 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  76 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__ge__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  77 (all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__le__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  78 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__of__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  79 (all V_y_2 all V_x_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(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)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  80 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  81 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_RealVector_Oreal__normed__field(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))) # label(fact_norm__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  82 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__0__le__divide__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  83 (all V_a all 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))) # label(fact_divide__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  84 (all V_a all 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))) # label(fact_divide__zero__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  85 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c))) # label(fact_times__divide__eq__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  86 (all V_c all V_b all V_a all 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)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  87 (all V_a all V_b all T_a (class_RealVector_Oreal__normed__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))))) # label(fact_nonzero__norm__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  88 (all V_y all 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))) # label(fact_divide_Ozero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  89 (all V_ya all V_y all V_x all 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)))) # label(fact_divide_Oadd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  90 (all V_b all V_a all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (hAPP(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))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  91 (all V_a all V_b all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (V_b = hAPP(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)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  92 (all V_ab_2 all V_b_2 all V_ca_2 all 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_ab_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  93 (all V_b_2 all V_ab_2 all V_ca_2 all T_a (class_Rings_Odivision__ring(T_a) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_ab_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2) = V_b_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  94 (all V_b_2 all V_ab_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2) <-> V_ab_2 = V_b_2))) # label(fact_real__mult__left__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  95 (all V_b_2 all V_ab_2 all V_ca_2 (V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ab_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2) <-> V_ab_2 = V_b_2))) # label(fact_real__mult__right__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  96 (all V_y all V_x all V_c (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(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)))) # label(fact_rabs__ratiotest__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  97 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)))) # label(fact_norm__ge__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  98 (all V_y_2 all V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(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))) # label(fact_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  99 (all V_x_2 all 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)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  100 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  101 (all V_c all V_b all V_a all 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)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  102 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2) <-> V_b_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  103 (all V_ca_2 all V_ab_2 all V_b_2 all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) <-> V_b_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  104 (all V_c all V_b all V_a all 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))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  105 (all V_c all V_b all V_a all 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))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  106 (all V_c all V_a all V_b all 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))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  107 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a))) # label(fact_abs__idempotent) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  108 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  109 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  110 (all V_b_2 all V_ab_2 all T_a (class_Rings_Oring__no__zero__divisors(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) | V_b_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  111 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  112 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(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)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  113 (all V_a all 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)) # label(fact_add__0__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  114 (all V_a all 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)) # label(fact_add__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  115 (all V_ab_2 all 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_ab_2,V_ab_2) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  116 (all V_a all 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)) # label(fact_add__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  117 (all V_a all 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)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  118 (all V_b_2 all V_ca_2 all V_ab_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  119 (all V_b_2 all V_ab_2 all V_ca_2 all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  120 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  121 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  122 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))) # label(fact_add__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  123 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  124 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,V_a,V_b)))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  125 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  126 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  127 (all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Groups_Oabs__class_Oabs(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__eq__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  128 (all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_abs__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  129 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)))) # label(fact_abs__ge__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  130 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)))) # label(fact_abs__le__D1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  131 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(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)))) # label(fact_abs__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  132 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(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_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) # label(fact_abs__mult__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  133 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__add__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  134 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))) # label(fact_zero__le__square) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  135 (all V_b_2 all V_ab_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  136 (all V_b_2 all V_ab_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  137 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  138 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonneg__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  139 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonneg__nonpos2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  140 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__nonpos__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  141 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  142 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  143 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  144 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  145 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  146 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  147 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  148 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  149 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  150 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_split__mult__neg__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  151 (all V_ab_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  152 (all V_ab_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  153 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  154 (all V_y_2 all V_x_2 all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  155 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  156 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  157 (all V_x all V_z all V_y all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y)))) # label(fact_add__num__frac) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  158 (all V_y all V_x all V_z all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z)))) # label(fact_add__divide__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  159 (all V_z all V_x all V_y all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y)))) # label(fact_add__frac__num) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  160 (all V_y all V_x all V_z all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z)))) # label(fact_divide__add__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  161 (all V_w all V_x all V_z all V_y all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  162 (all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_nonzero__abs__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  163 (all V_w_2 all V_x_2 all V_za_2 all V_y_2 all 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_w_2,V_za_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  164 (all V_b all V_a all V_c all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  165 (all V_b all V_a all V_c all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  166 (all V_y all V_x all 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))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  167 (all V_y all V_x all 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))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  168 (all V_y all V_x all 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)))) # label(fact_order__less__asym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  169 (all V_z all V_x all V_y all 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))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  170 (all V_z all V_y all V_x all 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))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  171 (all V_c all V_a all V_b all 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))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  172 (all V_c all V_b all V_a all 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))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  173 (all V_c all V_b all V_a all 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))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  174 (all V_c all V_b all V_a all 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))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  175 (all V_a all V_b all 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)))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  176 (all V_b all V_a all 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)))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  177 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  178 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  179 (all V_y all V_x all 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)))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  180 (all V_y all V_x all 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)))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  181 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  182 (all V_y all V_x all 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))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  183 (all V_x_2 all V_y_2 all 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)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  184 (all V_y all V_x all 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))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  185 (all V_y_2 all V_x_2 all 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))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  186 (all V_y_2 all V_x_2 all 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)))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  187 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  188 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  189 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  190 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_z,V_x))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  191 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_z))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  192 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.81  193 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (V_a != V_b -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  194 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  195 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  196 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  197 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_leD) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  198 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> c_Orderings_Oord__class_Oless(T_a,V_b,V_a))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  199 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  200 (all V_y_2 all V_x_2 all 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__eq(T_a,V_x_2,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  201 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) -> c_Orderings_Oord__class_Oless(T_a,V_x,V_y)))) # label(fact_not__leE) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  202 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)))) # label(fact_leI) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  203 (all V_y_2 all V_x_2 all T_a (class_Orderings_Oorder(T_a) -> (c_Orderings_Oord__class_Oless__eq(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))) # label(fact_order__le__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  204 (all V_y_2 all V_x_2 all 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__eq(T_a,V_x_2,V_y_2) & -c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  205 (all V_y_2 all V_x_2 all 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__eq(T_a,V_x_2,V_y_2) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  206 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) | c_Orderings_Oord__class_Oless(T_a,V_y,V_x))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  207 (all V_y_2 all V_x_2 all T_a (class_Orderings_Olinorder(T_a) -> (-c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  208 (all V_y_2 all V_x_2 all 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__eq(T_a,V_y_2,V_x_2)))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  209 (all V_b all V_a all V_c all 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)))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  210 (all V_b all V_c all V_a all 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)))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  211 (all V_d all V_c all V_b all V_a all 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)))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  212 (all V_c all V_b all V_a all 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))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  213 (all V_c all V_b all V_a all 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))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  214 (all V_b_2 all V_ab_2 all V_ca_2 all 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_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  215 (all V_b_2 all V_ca_2 all V_ab_2 all 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_ab_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_ab_2,V_b_2)))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  216 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(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)) # label(fact_less__eq__real__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  217 (all V_y_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) & V_x_2 != V_y_2)) # label(fact_real__less__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  218 (all V_c all V_a all V_b all 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)))))) # label(fact_divide__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  219 (all V_c all V_b all V_a all 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)))))) # label(fact_divide__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  220 (all V_y all V_x all 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)))))) # label(fact_divide__neg__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  221 (all V_y all V_x all 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)))))) # label(fact_divide__neg__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  222 (all V_y all V_x all 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)))))) # label(fact_divide__pos__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  223 (all V_y all V_x all 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)))))) # label(fact_divide__pos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  224 (all V_b_2 all V_ab_2 all 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_ab_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_ab_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_ab_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)))) # label(fact_divide__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  225 (all V_b_2 all V_ab_2 all 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_ab_2,V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_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_ab_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))))) # label(fact_zero__less__divide__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  226 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  227 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonneg__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  228 (all V_z all V_w all V_y all V_x all 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__eq(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)))))))) # label(fact_frac__less2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  229 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(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)))))))) # label(fact_frac__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  230 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)))))))) # label(fact_frac__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  231 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_divide__nonpos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  232 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_divide__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  233 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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_ab_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  234 (all V_ab_2 all V_ca_2 all V_b_2 all 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_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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_ab_2)))))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  235 (all V_b_2 all V_ab_2 all V_ca_2 all 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_ab_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),V_b_2))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  236 (all V_ab_2 all V_b_2 all V_ca_2 all 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_ab_2) <-> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2)))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  237 (all V_z all V_x all V_y all 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(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))))) # label(fact_mult__imp__div__pos__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  238 (all V_x all V_z all V_y all 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(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)))))) # label(fact_mult__imp__less__div__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  239 (all V_b_2 all V_ab_2 all V_ca_2 all 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_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2)))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  240 (all V_ab_2 all V_b_2 all V_ca_2 all 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_ab_2) <-> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),V_b_2))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  241 (all V_c all V_a all V_b all 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(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))))))) # label(fact_divide__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  242 (all V_c all V_b all V_a all 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(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))))))) # label(fact_divide__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  243 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__square__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  244 (all V_b_2 all V_ca_2 all V_ab_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(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_ab_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_ab_2)))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  245 (all V_b_2 all V_ab_2 all V_ca_2 all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(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_ab_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_ab_2)))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  246 (all V_b_2 all V_ab_2 all V_ca_2 all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  247 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  248 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  249 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  250 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  251 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(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))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  252 (all V_b_2 all V_ab_2 all V_ca_2 all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(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_ab_2))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  253 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  254 (all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  255 (all V_c all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  256 (all V_c all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  257 (all V_c all V_b all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  258 (all V_c all V_a all V_b all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  259 (all V_c all V_a all V_b all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  260 (all V_ab_2 all 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_ab_2,V_ab_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  261 (all V_ab_2 all 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_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  262 (all V_b all V_a all 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)))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  263 (all V_c all V_b all V_a all 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)))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  264 (all V_b all V_a all 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)))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  265 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  266 (all V_d all V_c all V_b all V_a all 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__eq(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)))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  267 (all V_x all V_y all 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))))) # label(fact_abs__div__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  268 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_abs__not__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  269 (all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_ab_2)) <-> V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__abs__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  270 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a))) # label(fact_abs__of__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  271 (all V_d all V_b all V_c all V_a all 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(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  272 (all V_y_2 all V_x_2 all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(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)))) # label(fact_real__mult__less__iff1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  273 (all V_y 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),V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))))) # label(fact_real__mult__order) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  274 (all V_y all V_x all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))))) # label(fact_real__mult__less__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  275 (all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_norm__not__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  276 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  277 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) -> (c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))))))) # label(fact_divide__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  278 (all V_ab_2 all V_b_2 all V_ca_2 all 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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_ab_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),V_b_2))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  279 (all V_b_2 all V_ab_2 all V_ca_2 all 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__eq(T_a,V_ab_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2)))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  280 (all V_x all V_z all V_y all 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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x) -> c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))))) # label(fact_mult__imp__le__div__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  281 (all V_z all V_x all V_y all 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__eq(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z))))) # label(fact_mult__imp__div__pos__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  282 (all V_ab_2 all V_b_2 all V_ca_2 all 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__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_ab_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2)))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  283 (all V_b_2 all V_ab_2 all V_ca_2 all 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__eq(T_a,V_ab_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),V_b_2))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  284 (all V_ab_2 all V_ca_2 all V_b_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_ab_2) <-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) -> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  285 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_ab_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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_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__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  286 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(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__eq(T_a,V_a,V_b))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  287 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(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__eq(T_a,V_a,V_b))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  288 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  289 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  290 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  291 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  292 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  293 (all V_d all V_c all V_b all V_a all 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__eq(T_a,V_c,V_d) -> (c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  294 (all V_d all V_c all V_b all V_a all 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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  295 (all V_d all V_c all V_b all V_a all 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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  296 (all V_b_2 all V_ab_2 all V_ca_2 all 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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_ab_2))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  297 (all V_b_2 all V_ab_2 all V_ca_2 all 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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  298 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  299 (all V_b all V_a all 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__eq(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)))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  300 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  301 (all V_c all V_b all V_a all 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__eq(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)))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  302 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  303 (all V_b all V_a all 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__eq(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)))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  304 (all V_y_2 all V_x_2 all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(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)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  305 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__sum__squares__lt__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  306 (all V_x_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_zero__less__norm__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  307 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)))))) # label(fact_norm__mult__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  308 (all V_y_2 all V_x_2 all 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__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  309 (all V_y_2 all V_x_2 all 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__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  310 (all V_s all V_y all V_r all V_x all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)))))) # label(fact_norm__add__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  311 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  312 (all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))) # label(fact_abs__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  313 (all V_b_2 all V_ab_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ab_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) | c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  314 (all V_b_2 all V_ab_2 all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  315 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))))) # label(fact_divide__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  316 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)))))) # label(fact_divide__right__mono__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  317 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_ab_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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2) = V_b_2) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  318 (all V_ab_2 all V_ca_2 all V_b_2 all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_ab_2 <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2)) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) -> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  319 v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> (exists B_r all B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_aa____,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____))),B_z))))) # label(fact_calculation) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  320 (all T_a (class_Groups_Ozero(T_a) -> c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_pCons__0__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  321 (all V_pa_2 all V_ab_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_pCons__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  322 (all V_x_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(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))) # label(fact_not__real__square__gt__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  323 (all V_ab_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) <-> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  324 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,B_x,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_divide_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  325 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_mult__left_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  326 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_mult__right_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  327 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  328 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  329 (all V_q_2 all V_pa_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2) <-> V_pa_2 = V_q_2))) # label(fact_poly__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  330 (all V_pa_2 all T_a (class_Int_Oring__char__0(T_a) & class_Rings_Oidom(T_a) -> (c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_poly__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  331 (all V_g_2 all V_f_2 all T_a all 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__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) & -c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)))) # label(fact_less__fun__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  332 (all V_x all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_poly__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  333 (all V_x all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))))) # label(fact_poly__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  334 (all V_p all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p)) # label(fact_add__poly__code_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  335 (all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  336 (all V_q all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q)) # label(fact_add__poly__code_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  337 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_mult__poly__0__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  338 (all V_q_2 all V_b_2 all V_pa_2 all V_ab_2 all T_a (class_Groups_Ozero(T_a) -> (c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2) <-> V_ab_2 = V_b_2 & V_pa_2 = V_q_2))) # label(fact_pCons__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  339 (all V_ab_2 all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  340 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)))) # label(fact_add__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  341 (all V_a all V_r c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(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)) # label(fact_real__divide__square__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  342 (all V_a all V_d (v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) -> (exists B_r all B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_d,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,V_a,v_cs____)),B_z))))))) # label(fact_pCons_Ohyps) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  343 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_a all B_b c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))))) # label(fact_mult_Opos__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  344 (all V_pa_2 all V_ab_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2)) <-> c_Polynomial_Opos__poly(T_a,V_pa_2) | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)))) # label(fact_pos__poly__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  345 (all V_p all V_r exists B_m (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) & (all B_z (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),B_m))))) # label(fact_poly__bound__exists) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  346 (all V_ab_2 all V_pa_2 all T_a (class_Rings_Oidom(T_a) -> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ab_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) | c_Polynomial_Oorder(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_order__root) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  347 (all V_pa_2 all V_ab_2 all T_a all V_za_2 all V_f_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2) = V_za_2 -> c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,V_pa_2))))) # label(fact_poly__rec__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  348 (all V_r all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)))) # label(fact_mult__poly__add__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  349 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)))))) # label(fact_pos__poly__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  350 (all V_q all V_p all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Polynomial_Opos__poly(T_a,V_p) -> (c_Polynomial_Opos__poly(T_a,V_q) -> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))))) # label(fact_pos__poly__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  351 (all T_a (class_Rings_Olinordered__idom(T_a) -> -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_not__pos__poly__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  352 (all T_a all V_za_2 all V_f_2 all T_b (class_Groups_Ozero(T_b) -> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2) = V_za_2 -> c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_za_2))) # label(fact_poly__rec__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  353 (all V_pa_2 all V_ab_2 all V_f_2 all V_za_2 all T_a all T_b (class_Groups_Ozero(T_b) -> c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2,c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,V_pa_2))))) # label(fact_poly__rec_Osimps) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  354 (all V_q all V_p all V_a all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))))) # label(fact_pcompose__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  355 (all V_pa_2 all T_a (class_Groups_Ozero(T_a) -> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_psize__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  356 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__zeroE) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  357 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_le0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  358 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,B_x,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_divide_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  359 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  360 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  361 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  362 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (V_m != V_n -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  363 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) | V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  364 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__not__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  365 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  366 (all V_y all 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)))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  367 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  368 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  369 (all V_t all V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  370 (all V_P_2 all V_n_2 all V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  371 (all V_k all V_j all 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))) # label(fact_add__lessD1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.82  372 (all V_n all V_m all V_l all 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)))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  373 (all V_l all V_k all V_j all 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))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  374 (all V_k all V_j all 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)))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  375 (all V_m all V_j all 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)))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  376 (all V_m all V_j all 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)))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  377 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  378 (all V_i all V_j -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)) # label(fact_not__add__less2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  379 (all V_j all V_i -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)) # label(fact_not__add__less1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  380 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) # label(fact_le__square) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  381 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))) # label(fact_le__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  382 (all V_m all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))) # label(fact_le__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  383 (all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) # label(fact_le__cube) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  384 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_le__Suc__ex__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  385 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) <-> (exists B_k V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  386 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  387 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  388 (all V_m all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  389 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  390 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  391 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  392 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  393 (all V_l all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  394 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n))) # label(fact_add__leD2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  395 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_add__leD1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  396 (all V_n all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) -> -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_add__leE) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  397 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  398 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)))) # label(fact_le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  399 (all V_n all V_m (V_m = V_n -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  400 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  401 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n)) # label(fact_le__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  402 (all V_q all T_a (class_Rings_Ocomm__semiring__0(T_a) -> c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) # label(fact_pcompose__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  403 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__semiring__0(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__pcompose) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  404 (all V_n hAPP(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)) # label(fact_mult__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  405 (all V_n c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  406 (all V_n c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  407 (all V_m hAPP(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)) # label(fact_mult__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  408 (all V_m c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  409 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(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))) # label(fact_le__0__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  410 (all V_n_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  411 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  412 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  413 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  414 (all V_n all 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))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  415 (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))) # label(fact_gr0I) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  416 (all V_k all V_j all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  417 (all V_k all V_j all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  418 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  419 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(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__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  420 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  421 (all V_n_2 all V_k_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(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_m_2,V_n_2))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  422 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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_m_2,V_n_2))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  423 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  424 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  425 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_add__gr__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  426 (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))) # label(fact_neq0__conv) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  427 (all V_n -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_not__less0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  428 (all V_n_2 all V_m_2 all 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__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  429 (all V_y all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  430 (all V_n_2 all V_m_2 all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  431 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  432 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_a all B_b c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))))) # label(fact_mult_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  433 (all V_n_2 all V_k_2 all V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  434 (all V_n_2 all V_m_2 all V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  435 (all V_k all V_n all V_m hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  436 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  437 (all V_k all V_n all 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))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  438 (all V_n all V_m all V_k hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  439 (all V_z all V_y all 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))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  440 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  441 (all V_n all 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)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  442 (all V_k all V_j all V_u all V_i c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(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)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  443 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(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_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  444 (all V_z all V_y all 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)))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  445 (all V_y all V_z all 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)))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  446 (all V_y all V_z all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  447 (all V_z all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  448 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  449 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))) # label(fact_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  450 (all V_y all T_a (class_RealVector_Oreal__normed__field(T_a) -> (exists B_K all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,B_x,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))) # label(fact_divide_Obounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  451 (all V_y all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))) # label(fact_mult__left_Obounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  452 (all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_a all B_b c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))) # label(fact_mult_Obounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  453 (all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> (exists B_K all B_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))) # label(fact_mult__right_Obounded) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  454 (all V_v all V_u all V_y all V_a all V_x all 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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  455 (all V_y all V_x all 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__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_field__le__epsilon) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  456 (all V_x_2 all 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)))) # label(fact_one__reorient) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  457 (all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_norm__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  458 (all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) # label(fact_one__poly__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  459 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a))) # label(fact_poly__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  460 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z) # label(fact_real__mult__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  461 (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))) # label(fact_abs__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  462 (all V_a all 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)) # label(fact_divide__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  463 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  464 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  465 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  466 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  467 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  468 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  469 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  470 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  471 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  472 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  473 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  474 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  475 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  476 (all T_a (class_Rings_Olinordered__semidom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_zero__le__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  477 (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)))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  478 (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)))) # label(fact_zero__less__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  479 (all V_n all V_m all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  480 (all V_a all 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))))) # label(fact_less__add__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  481 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  482 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  483 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(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))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  484 (all V_ab_2 all V_b_2 all 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_ab_2,V_b_2) = c_Groups_Oone__class_Oone(T_a) <-> V_ab_2 = V_b_2)))) # label(fact_right__inverse__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  485 (all V_a all 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)))) # label(fact_divide__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  486 (all V_a all 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)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  487 (all V_n all V_m (V_m = hAPP(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))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  488 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)))))) # label(fact_mult__left__le__one__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  489 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x)))))) # label(fact_mult__right__le__one__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  490 (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))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  491 (all V_b all V_a all 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)))) # label(fact_gt__half__sum) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  492 (all V_b all V_a all 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))))))) # label(fact_less__half__sum) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  493 (all V_x -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) # label(fact_abs__add__one__not__less__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  494 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u) -> (c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  495 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))) # label(fact_abs__add__one__gt__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  496 (all V_y all V_x all 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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x),V_y)))) -> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)))) # label(fact_field__le__mult__one__interval) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  497 (all V_n_2 all V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_P_2,V_n_2)) -> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) & (all B_i (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) -> -hBOOL(hAPP(V_P_2,B_i)))) & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  498 (all V_x all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x) = c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)))))) # label(fact_real__root__pos__mult__exp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  499 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)))))) # label(fact_real__root__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  500 (all V_n c_NthRoot_Oroot(V_n,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_real__root__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  501 (all V_y_2 all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_NthRoot_Oroot(V_n_2,V_x_2) = c_NthRoot_Oroot(V_n_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_real__root__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  502 (all V_x all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)) = c_NthRoot_Oroot(V_n,c_NthRoot_Oroot(V_m,V_x))))) # label(fact_real__root__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  503 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_NthRoot_Oroot(V_n_2,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_real__root__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  504 (all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_n,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) # label(fact_real__root__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  505 (all V_y_2 all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__root__le__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  506 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_n,V_y))))) # label(fact_real__root__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  507 (all V_y_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)))) # label(fact_real__root__ge__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  508 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_real__root__le__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  509 (all V_x all V_N all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x),c_NthRoot_Oroot(V_n,V_x)))))) # label(fact_real__root__decreasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  510 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_NthRoot_Oroot(V_n_2,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) # label(fact_real__root__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  511 (all V_y_2 all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)))) # label(fact_real__root__less__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  512 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_n,V_y))))) # label(fact_real__root__less__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  513 (all V_y_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)))) # label(fact_real__root__gt__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  514 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,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))))) # label(fact_real__root__lt__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  515 (all V_x all V_N all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (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_NthRoot_Oroot(V_N,V_x),c_NthRoot_Oroot(V_n,V_x)))))) # label(fact_real__root__strict__decreasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  516 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)))) # label(fact_real__root__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  517 (all V_x all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x) = c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x))))) # label(fact_real__root__mult__exp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  518 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_n,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_n,V_y)))) # label(fact_real__root__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  519 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_n,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)))) # label(fact_real__root__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  520 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x))))) # label(fact_real__root__ge__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  521 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))) # label(fact_real__root__le__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  522 (all V_y_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)))) # label(fact_real__root__ge__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  523 (all V_x all V_N all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_N,V_x))))))) # label(fact_real__root__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  524 (all V_y_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n_2,V_y_2)) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)))) # label(fact_real__root__gt__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  525 (all V_x_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,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))))) # label(fact_real__root__lt__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  526 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x))))) # label(fact_real__root__gt__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  527 (all V_x all V_N all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N) -> (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,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_N,V_x))))))) # label(fact_real__root__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  528 (all V_y all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x),c_NthRoot_Oroot(V_n,V_y)))))) # label(fact_real__root__less__mono__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  529 (all V_x_1 all V_n_1 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_1) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_1) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n_1,V_x_1))))) # label(fact_real__root__pos__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  530 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natceiling__add__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  531 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_natfloor__add__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  532 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n) = V_x))) # label(fact_real__root__pow__pos) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  533 (all V_x all V_y all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) -> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),V_n) = V_x -> c_NthRoot_Oroot(V_n,V_x) = V_y)))) # label(fact_real__root__pos__unique) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  534 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  535 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__algebra__1(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)))) # label(fact_norm__power__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  536 (all V_n all V_x all T_a (class_RealVector_Oreal__normed__div__algebra(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) # label(fact_norm__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  537 (all V_x all V_n all V_p all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n))) # label(fact_poly__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  538 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  539 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  540 (all V_x c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))) # label(fact_zero__le__natfloor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  541 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)))) # label(fact_natfloor__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  542 (all V_x c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x))) # label(fact_zero__le__natceiling) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  543 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)))) # label(fact_natceiling__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  544 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  545 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  546 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natfloor__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  547 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) -> c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_natceiling__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  548 (all V_k all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_k))) # label(fact_real__root__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  549 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))) # label(fact_le__natfloor__eq__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  550 (all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_natceiling__le__eq__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  551 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))))) # label(fact_le__mult__natfloor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  552 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = V_x))) # label(fact_real__root__pos2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  553 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n) = V_x))) # label(fact_real__root__pow__pos2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  554 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  555 (all V_n all V_a all 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_one__less__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  556 (all V_y_2 all V_x_2 all V_b_2 all 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__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  557 (all V_n all V_m all V_a all 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__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n))))) # label(fact_power__le__imp__le__exp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  558 (all V_n_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)) <-> V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  559 (all V_n_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  560 (all V_n all V_m all 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))) # label(fact_nat__power__less__imp__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  561 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  562 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  563 (all V_n all V_a all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_field__power__not__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  564 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  565 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  566 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  567 (all V_n all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  568 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) # label(fact_power__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  569 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  570 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a)) # label(fact_power__one__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  571 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  572 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))) # label(fact_power__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  573 (all V_n all V_a all 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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  574 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_one__le__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  575 (all V_n_2 all V_ab_2 all T_a (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  576 (all V_n_2 all V_m_2 all V_ab_2 all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ab_2) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) <-> V_m_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  577 (all V_n all V_a all V_b all T_a (class_Fields_Ofield(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))) # label(fact_nonzero__power__divide) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  578 (all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  579 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  580 (all V_n all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(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))) # label(fact_power__one__over) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  581 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) -> c_Orderings_Oord__class_Oless(T_a,V_a,V_b))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  582 (all V_n all V_a all 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  583 (all V_n all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  584 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(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) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  585 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)))) # label(fact_zero__le__power__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  586 (all V_a all V_N all V_n all 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  587 (all V_n all V_m all V_a all 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))))) # label(fact_power__less__imp__less__exp) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  588 (all V_y_2 all V_x_2 all V_b_2 all 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(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))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  589 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))) # label(fact_power__increasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  590 (all V_n all V_a all 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(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  591 (all V_a all V_N all V_n all 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.83  592 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(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)))))) # label(fact_power__eq__imp__eq__base) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  593 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  594 (all V_n all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (exists B_z c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))) # label(fact_reduce__poly__simple) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  595 (all T_a (class_Power_Opower(T_a) -> c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)))) # label(fact_power__power__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  596 (all V_x all V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_natceiling__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  597 (all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__ge__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  598 (all V_n all V_x c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))) # label(fact_zero__le__zpower__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  599 (all V_n all V_m hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))) # label(fact_power__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  600 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)) # label(fact_real__of__nat__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  601 (all V_za_2 (c_Orderings_Oord__class_Oless__eq(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))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  602 (all V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint)) <-> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zabs__less__one__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  603 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  604 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  605 (all V_n all V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) -> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_abs__zmult__eq__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  606 (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)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  607 (all V_za_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_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_w_2,V_za_2) | V_w_2 = V_za_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  608 (all V_z all V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  609 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  610 (all V_z (c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  611 (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)))) # label(fact_odd__less__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  612 (all V_za_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_za_2))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  613 (all V_za_2 all V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_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__eq(tc_Int_Oint,V_w_2,V_za_2))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  614 (all V_w_2 all V_za_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2) & V_za_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  615 (all V_y all 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))) # label(fact_zless__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  616 (all V_m_2 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2) <-> V_n_2 = V_m_2)) # label(fact_real__of__nat__inject) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  617 (all V_x c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x)) # label(fact_abs__real__of__nat__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  618 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  619 (all V_z2 all V_z1 all V_w hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  620 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  621 (all V_w all V_z2 all V_z1 hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  622 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  623 (all V_z c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  624 (all V_k all V_j all 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)))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  625 (all V_z all V_z_H all V_w all V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) -> (c_Orderings_Oord__class_Oless__eq(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))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  626 (all V_k all V_j all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  627 (all V_n c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natceiling__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  628 (all V_n c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n) # label(fact_natfloor__real__of__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  629 (all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__zero__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  630 (all V_n -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) # label(fact_not__real__of__nat__less__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  631 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_real__of__nat__less__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  632 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2))) # label(fact_real__of__nat__le__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  633 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  634 (all V_n all V_m c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))) # label(fact_real__of__nat__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  635 (all V_n all V_x (V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) -> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n))) # label(fact_natfloor__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  636 (all V_x c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))) # label(fact_real__natceiling__ge) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  637 (all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  638 (all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x))) # label(fact_real__natfloor__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  639 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)))) # label(fact_le__natfloor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  640 (all V_ab_2 all V_times_2 all V_one_2 all T_a hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2) # label(fact_power_Opower_Opower__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  641 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a))) # label(fact_natceiling__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  642 (all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) <-> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  643 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))) # label(fact_nat__less__real__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  644 (all V_m_2 all V_n_2 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) <-> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) # label(fact_nat__le__real__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  645 (all V_ab_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ab_2,c_RComplete_Onatfloor(V_x_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2),V_x_2)))) # label(fact_le__natfloor__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  646 (all V_ab_2 all V_x_2 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_ab_2) <-> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2))))) # label(fact_natceiling__le__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  647 (all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) # label(fact_real__natfloor__add__one__gt) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  648 (all V_n all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n)) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)))) # label(fact_less__natfloor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  649 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a))) # label(fact_natfloor__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  650 (all V_n all V_z (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)))) # label(fact_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  651 (all V_x all V_n (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) -> c_RComplete_Onatfloor(V_x) = V_n))) # label(fact_natfloor__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  652 (all V_a all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a))) # label(fact_natceiling__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  653 (all V_n all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)))) # label(fact_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  654 (all V_n_2 all V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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))) # label(fact_zero__less__power__nat__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  655 (all V_q all V_r all 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(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__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q))))) # label(fact_self__quotient__aux1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  656 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> c_Orderings_Oord__class_Oless__eq(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)))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  657 (all V_z3 all V_z2 all 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))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  658 (all V_z all V_y all 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))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  659 (all V_w all 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)) # label(fact_zadd__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  660 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  661 (all V_k all V_j all V_i (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)))) # label(fact_zle__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  662 (all V_w all V_z (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z))) # label(fact_zle__linear) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  663 (all V_w c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w)) # label(fact_zle__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  664 (all V_r_H all V_q_H all V_b_H (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H))))) # label(fact_q__pos__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  665 (all V_r_H all V_q_H all V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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__eq(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__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_q__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  666 (all V_r all V_q all V_r_H all V_q_H all V_b (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) -> (c_Orderings_Oord__class_Oless__eq(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__eq(tc_Int_Oint,V_q_H,V_q)))))) # label(fact_unique__quotient__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  667 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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__eq(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__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)))))))) # label(fact_zdiv__mono2__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  668 (all V_r all V_q all V_r_H all V_q_H all V_b (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) -> (c_Orderings_Oord__class_Oless__eq(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__eq(tc_Int_Oint,V_q,V_q_H)))))) # label(fact_unique__quotient__lemma__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  669 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(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(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__eq(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__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)))))))) # label(fact_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  670 (all V_q all V_r all 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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) # label(fact_self__quotient__aux2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  671 (all V_n all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  672 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  673 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  674 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y) -> c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y)))) # label(fact_natfloor__div__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  675 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Odecseq(T_a,V_X_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))))))) # label(fact_decseq__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  676 (all V_a all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> (exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a & (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a -> B_y = B_x))))))) # label(fact_realpow__pos__nth__unique) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  677 (all V_n all V_m all V_k ((V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)))) # label(fact_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  678 (all V_k all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)))) # label(fact_div__le__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  679 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_div__le__dividend) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  680 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)) # label(fact_div__mult2__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  681 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_div__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  682 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  683 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__by__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  684 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_div__by__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  685 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  686 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  687 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a))) # label(fact_div__mult__self1__is__id) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  688 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a))) # label(fact_div__mult__self2__is__id) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  689 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c = c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)) & (V_c != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))) # label(fact_div__mult__mult1__if) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  690 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_div__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  691 (all V_k all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))))) # label(fact_div__le__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  692 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m)) # label(fact_div__mult__self__is__m) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  693 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m)) # label(fact_div__mult__self1__is__m) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  694 (all V_n all V_m all V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))) # label(fact_nat__mult__div__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  695 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)))) # label(fact_div__less__dividend) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  696 (all V_x all V_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)))) # label(fact_real__of__nat__div4) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  697 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  698 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))))) # label(fact_div__mult__self1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  699 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  700 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  701 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) -> (V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j) -> hBOOL(hAPP(V_P_2,B_i)))))))) # label(fact_split__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  702 (all V_a all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) -> (exists B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a))))) # label(fact_realpow__pos__nth) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  703 (all V_x all V_d (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_d) -> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_d)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_d)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_d)),c_RealDef_Oreal(tc_Nat_Onat,V_d))))) # label(fact_real__of__nat__div__aux) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  704 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) <-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K))))))) # label(fact_Bseq__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  705 (all V_z all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z))) # label(fact_poly__div__mult__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  706 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))) # label(fact_div__add1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  707 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__div__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  708 (all V_b c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zdiv__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  709 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  710 (all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__neg__pos__less0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  711 (all V_ab_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2)))) # label(fact_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  712 (all V_ab_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  713 (all V_a (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zdiv__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  714 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__by__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  715 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m)) # label(fact_mod__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  716 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  717 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_mod__by__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  718 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  719 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_mod__less__divisor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  720 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  721 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  722 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  723 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  724 (all V_db_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_db_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> (exists B_q V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_db_2),B_q)))) # label(fact_mod__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  725 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__right__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  726 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__mult__left__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  727 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  728 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)))) # label(fact_mod__mult__mult1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  729 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c))) # label(fact_mod__mult__mult2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  730 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  731 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__mult__cong) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  732 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) # label(fact_mod__mult__self3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  733 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_mod__mult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  734 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_mod__mult__distrib2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  735 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  736 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  737 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  738 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  739 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  740 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  741 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  742 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  743 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mod__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  744 (all V_n all V_m c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m)) # label(fact_mod__less__eq__dividend) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  745 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a)) # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  746 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  747 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  748 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))) # label(fact_div__mod__equality2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  749 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))) # label(fact_div__mod__equality) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  750 (all V_b all V_a_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))) # label(fact_zdiv__mono1__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  751 (all V_b all V_a_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))))) # label(fact_zdiv__mono1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  752 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__neg__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  753 (all V_b all V_b_H all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))))) # label(fact_zdiv__mono2__neg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  754 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__nonpos__pos__le0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  755 (all V_ab_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  756 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__pos__pos__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  757 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_div__nonneg__neg__le0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  758 (all V_b all V_b_H all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)))))) # label(fact_zdiv__mono2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  759 (all V_b_2 all V_ab_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_ab_2) & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)))) # label(fact_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  760 (all V_i_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2)))) # label(fact_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  761 (all V_ab_2 all V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) <-> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2)))) # label(fact_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  762 (all V_k_2 all V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2))) # label(fact_zdiv__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  763 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n))) # label(fact_mod__le__divisor) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  764 (all V_k all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x)))) # label(fact_int__div__less__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  765 (all V_b all V_a all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))) # label(fact_zdiv__zmult2__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  766 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))) # label(fact_div__mult1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  767 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b))) # label(fact_mod__mult2__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  768 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))))) # label(fact_mod__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  769 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_P_2,V_n_2))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) -> (V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j) -> hBOOL(hAPP(V_P_2,B_j)))))))) # label(fact_split__mod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  770 (all V_r_1 all V_y all V_b_1 all V_a_1 (V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1) -> ((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__div__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  771 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (all B_i ((exists B_j (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (all B_i ((exists B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j))) -> hBOOL(hAPP(V_P_2,B_i))))))) # label(fact_split__zdiv) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  772 (all V_X_2 all V_K_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2) -> ((all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)) -> c_SEQ_OBseq(T_a,V_X_2))))) # label(fact_BseqI) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  773 (all V_X_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> (c_SEQ_OBseq(T_a,V_X_2) -> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) & (all B_n c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K))))))) # label(fact_BseqD) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  774 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zadd1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  775 (all V_b all V_a V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zdiv__equality) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  776 (all V_c all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))) # label(fact_zdiv__zmult1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  777 (all V_k all V_a all V_b c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k)) # label(fact_zdiv__zmod__equality) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  778 (all V_k all V_b all V_a c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k)) # label(fact_zdiv__zmod__equality2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.84  779 (all V_b all V_a c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zdiv__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  780 (all V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a)) # label(fact_DIVISION__BY__ZERO) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  781 (all V_y all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m)) # label(fact_zpower__zmod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  782 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b))) # label(fact_pos__mod__bound) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  783 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_neg__mod__bound) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  784 (all V_y all V_x (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  785 (all V_k all V_m (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m))) # label(fact_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  786 (all V_b c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  787 (all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  788 (all V_db_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_db_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> (exists B_q V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_db_2),B_q)))) # label(fact_zmod__eq__0__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  789 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)) # label(fact_zmod__simps_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  790 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) # label(fact_zmod__zmult1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  791 (all V_z all V_y all V_x all T_a (class_Fields_Ofield(T_a) -> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))) # label(fact_poly__mod__mult__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  792 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_pos__mod__sign) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  793 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b))) # label(fact_pos__mod__conj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  794 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__pos__pos__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  795 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_neg__mod__sign) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  796 (all V_a all V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_neg__mod__conj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  797 (all V_b all V_a (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__neg__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  798 (all V_b all V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b)))) # label(fact_mod__pos__neg__trivial) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  799 (all V_b all V_a all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_zmod__zmult2__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  800 (all V_k_2 all V_n_2 all V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_P_2,V_n_2))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (all B_i all B_j (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) -> hBOOL(hAPP(V_P_2,B_j))))) & (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) -> hBOOL(hAPP(V_P_2,B_j))))))) # label(fact_split__zmod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  801 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)))))) # label(fact_zmult2__lemma__aux3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  802 (all V_q all V_b all V_r all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)))))) # label(fact_zmult2__lemma__aux4) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  803 (all V_q all V_r all V_b all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)))))) # label(fact_zmult2__lemma__aux1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  804 (all V_q all V_r all V_b all V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_zmult2__lemma__aux2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  805 (all V_y all V_q_1 all V_b_1 all V_a_1 (V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1),V_y) -> ((c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y) & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_b_1)) & (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_y) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  806 (all V_n_2 all V_P_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) -> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__neg__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  807 (all V_n_2 all V_P_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) -> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2) & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) -> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))))))) # label(fact_split__pos__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  808 (all V_X_2 all T_a (class_Orderings_Oorder(T_a) -> (c_SEQ_Oincseq(T_a,V_X_2) <-> (all B_m all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) -> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))))) # label(fact_incseq__def) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  809 (all V_K_2 all V_X_2 all V_N_2 all T_a (class_RealVector_Oreal__normed__vector(T_a) -> ((all B_n (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2,B_n) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2))) -> c_SEQ_OBseq(T_a,V_X_2)))) # label(fact_BseqI2_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  810 (all V_n all V_d (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_d) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_d,V_n) -> c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_d)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_d))))) # label(fact_real__of__nat__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  811 (all V_y all V_n all V_x (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y,V_x) -> (exists B_q V_x = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)))))) # label(fact_nat__mod__eq__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  812 (all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x)) # label(fact_dvd_Oorder__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  813 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  814 (all V_b_2 all V_ab_2 all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) <-> c_Divides_Odiv__class_Omod(T_a,V_b_2,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  815 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__imp__mod__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  816 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n) -> c_Rings_Odvd__class_Odvd(T_a,V_k,V_m))))) # label(fact_dvd__mod__imp__dvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  817 (all V_n all V_m all V_k all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_m) -> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n) -> c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))))) # label(fact_dvd__mod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  818 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_b) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c)))) # label(fact_mod__mod__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  819 (all V_m_2 all V_n_2 all V_k_2 all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_n_2) -> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_n_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2))))) # label(fact_dvd__mod__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  820 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) -> -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)))) # label(fact_nat__dvd__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  821 (all V_n_2 all V_m_2 all V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(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) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2))) # label(fact_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  822 (all V_n all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y) -> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))))) # label(fact_dvd__power__same) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  823 (all V_k all V_l all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Groups_Oabs__class_Oabs(T_a,V_l) = c_Groups_Oabs__class_Oabs(T_a,V_k) -> c_Rings_Odvd__class_Odvd(T_a,V_l,V_k)))) # label(fact_dvd__if__abs__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  824 (all V_k_2 all V_m_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_m_2),V_k_2) <-> c_Rings_Odvd__class_Odvd(T_a,V_m_2,V_k_2)))) # label(fact_abs__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  825 (all V_k_2 all V_m_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_m_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_m_2,V_k_2)))) # label(fact_dvd__abs__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  826 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__0__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  827 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))) # label(fact_dvd__triv__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  828 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))) # label(fact_dvd__triv__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  829 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))) # label(fact_dvd__mult2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  830 (all V_b all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))) # label(fact_dvd__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  831 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_d) -> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))) # label(fact_mult__dvd__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  832 (all V_k all V_b all V_a all T_a (class_Rings_Odvd(T_a) -> (V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) -> c_Rings_Odvd__class_Odvd(T_a,V_b,V_a)))) # label(fact_dvdI) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  833 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)))) # label(fact_dvd__mult__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  834 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)))) # label(fact_dvd__mult__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  835 (all V_b_2 all V_ca_2 all V_ab_2 all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) | c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)))) # label(fact_dvd__mult__cancel__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  836 (all V_b_2 all V_ab_2 all V_ca_2 all T_a (class_Rings_Oidom(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) | c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)))) # label(fact_dvd__mult__cancel__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  837 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_a))) # label(fact_dvd__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  838 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c))))) # label(fact_dvd__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  839 (all V_y_2 all V_x_2 (V_x_2 = V_y_2 <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2))) # label(fact_dvd_Oeq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  840 (all V_y_2 all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) | V_x_2 = V_y_2)) # label(fact_dvd_Ole__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  841 (all V_y_2 all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) & V_x_2 != V_y_2)) # label(fact_dvd_Oless__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  842 (all V_b all V_a (V_a != V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)))) # label(fact_dvd_Oneq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  843 (all V_y all V_x (V_x = V_y -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))) # label(fact_dvd_Oeq__refl) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  844 (all V_x_2 all V_y_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_dvd_Oantisym__conv) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  845 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) | V_x = V_y)) # label(fact_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  846 (all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> (V_a != V_b -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)))) # label(fact_dvd_Ole__neq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  847 (all V_c all V_b all V_a (V_a = V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)))) # label(fact_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  848 (all V_c all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) -> (V_b = V_c -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)))) # label(fact_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  849 (all V_n all V_m (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) -> V_m = V_n))) # label(fact_dvd__antisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  850 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> V_x = V_y))) # label(fact_dvd_Oantisym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  851 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)))) # label(fact_dvd_Oorder__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  852 (all V_c all V_b all V_a (V_a = V_b -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)))) # label(fact_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  853 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Ole__less__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  854 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> V_x != V_y)) # label(fact_dvd_Oless__imp__neq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  855 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)))) # label(fact_dvd_Oless__not__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  856 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))) # label(fact_dvd_Oless__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  857 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)))) # label(fact_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  858 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> V_x != V_y)) # label(fact_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  859 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> V_y != V_x)) # label(fact_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  860 (all V_c all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) -> (V_b = V_c -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)))) # label(fact_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  861 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Oless__le__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  862 (all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)))) # label(fact_dvd_Oless__asym_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  863 (all V_z all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)))) # label(fact_dvd_Oless__trans) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  864 (all V_y all V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) -> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) & -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)))) # label(fact_dvd_Oless__asym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  865 (all V_a all V_n all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))) # label(fact_le__imp__power__dvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  866 (all V_m all V_n all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) -> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)))))) # label(fact_dvd__power__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  867 (all V_m all V_b all V_n all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b) -> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) -> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b))))) # label(fact_power__le__dvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  868 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) -> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))))) # label(fact_dvd__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  869 (all V_n_2 all V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2))) # label(fact_dvd__reduce) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  870 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a))) # label(fact_one__dvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  871 (all V_m_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__dvd__1__iff__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  872 (all V_n all V_x all V_y all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))))) # label(fact_div__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  873 (all V_w all V_z all V_x all V_y all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x) -> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_w) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_div__mult__div__if__dvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  874 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a)))) # label(fact_dvd__div__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  875 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b))) # label(fact_dvd__div__mult__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  876 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)))) # label(fact_div__mult__swap) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  877 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b))) # label(fact_dvd__mult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  878 (all V_y all V_x all V_z all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_x) -> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_y) -> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)))))) # label(fact_div__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  879 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Divides_Osemiring__div(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) -> (c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_ca_2) -> (c_Rings_Odvd__class_Odvd(T_a,c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2),c_Divides_Odiv__class_Odiv(T_a,V_ca_2,V_ab_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_b_2,V_ca_2)))))) # label(fact_div__dvd__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  880 (all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Divides_Osemiring__div(T_a) -> (V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) -> (c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = V_ca_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2)))))) # label(fact_dvd__div__eq__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  881 (all V_db_2 all V_b_2 all V_ca_2 all V_ab_2 all T_a (class_Divides_Osemiring__div(T_a) -> (V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) -> (c_Rings_Odvd__class_Odvd(T_a,V_ca_2,V_db_2) -> (c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = c_Divides_Odiv__class_Odiv(T_a,V_db_2,V_ca_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2)))))))) # label(fact_dvd__div__div__eq__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  882 (all V_n all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)))) # label(fact_dvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  883 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)))) # label(fact_dvd__mult__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  884 (all V_n_2 all V_m_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  885 (all V_x all V_n all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) | V_x = c_Groups_Oone__class_Oone(T_a) -> c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))))) # label(fact_dvd__power) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  886 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2),V_m_2) <-> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_dvd__mult__cancel2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  887 (all V_n_2 all V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2),V_m_2) <-> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_dvd__mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  888 (all V_n all V_m all V_i (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) -> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i) -> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)))) # label(fact_power__dvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  889 (all V_l_2 all V_P_2 all T_a (class_Rings_Odvd(T_a) & class_Rings_Osemiring__0(T_a) -> ((exists B_x hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))) <-> (exists B_x (c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(V_P_2,B_x))))))) # label(fact_unity__coeff__ex) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  890 (all V_b_2 all V_ab_2 all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)) <-> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ab_2,V_b_2)))) # label(fact_pow__divides__eq__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  891 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n) -> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m)))) # label(fact_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  892 (all V_n all V_m all V_f (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_m) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_n) -> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))))) # label(fact_zdvd__zmod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  893 (all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint)) <-> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zdvd1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  894 (all V_b_2 all V_ab_2 all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)) <-> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_b_2)))) # label(fact_pow__divides__eq__int) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  895 (all V_b all V_n all V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)))) # label(fact_pow__divides__pow__int) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  896 (all V_b all V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a) -> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b)))) # label(fact_zdvd__antisym__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  897 (all V_t_2 all V_m_2 all V_k_2 (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2) <-> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))))) # label(fact_zdvd__mono) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  898 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)) -> (V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)))) # label(fact_zdvd__mult__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  899 (all V_n all V_m (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n) -> -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)))) # label(fact_zdvd__not__zless) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  900 (all V_ca_2 all V_t_2 all V_x_2 all V_db_2 all V_ab_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_db_2) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)) <-> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_db_2)),V_t_2))))) # label(fact_zdvd__period) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  901 (all V_m_2 all V_n_2 all V_k_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))) <-> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2))) # label(fact_zdvd__reduce) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  902 (all V_n all V_m (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) -> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) -> V_m = V_n))))) # label(fact_zdvd__antisym__nonneg) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  903 (all V_x all V_y (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_y,V_x) -> c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_y)))) # label(fact_abs__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  904 (all V_m all V_n (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m)) # label(fact_zdvd__mult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  905 (all V_n all V_z (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n) -> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n)))) # label(fact_zdvd__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  906 (all V_d all V_i (V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i) -> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i))))) # label(fact_dvd__imp__le__int) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  907 (all V_n_2 all V_m_2 (V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2),V_m_2) <-> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_zdvd__mult__cancel1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  908 (all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  909 (all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x)) # label(fact_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  910 (all V_m all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) -> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) -> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)))) # label(fact_dvd__pos__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  911 (all V_b all V_n all V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)) -> (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)))) # label(fact_pow__divides__pow__nat) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  912 (all V_k_2 all V_P_2 all 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__eq(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(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_db_2)))))))))) # label(fact_incr__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  913 (all V_z all V_x all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z))) # label(fact_decr__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  914 (all V_y_2 all V_n_2 all V_x_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2) <-> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_zmod__eq__dvd__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  915 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y) -> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_z) -> c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)))))) # label(fact_dvd__diff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  916 (all V_n all V_m all V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)) -> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n) -> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m)))) # label(fact_zdvd__zdiffD) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  917 (all V_t_2 all V_D_2 all V_db_2 all T_a (class_Rings_Ocomm__ring(T_a) & class_Rings_Odvd(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2) -> (all B_x all B_k (c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))))))) # label(fact_inf__period_I3_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  918 (all V_t_2 all V_D_2 all V_db_2 all T_a (class_Rings_Ocomm__ring(T_a) & class_Rings_Odvd(T_a) -> (c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2) -> (all B_x all B_k (c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) <-> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))))))) # label(fact_inf__period_I4_J) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  919 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2)))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  920 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  921 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2)))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  922 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oordered__ring(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) <-> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  923 (all V_x all T_a (class_Rings_Oring__1(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))))) # label(fact_real__squared__diff__one__factored) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  924 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z)))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  925 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z)))) # label(fact_divide__diff__eq__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  926 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_diff__frac__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  927 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))) # label(fact_abs__diff__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  928 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))))) # label(fact_abs__triangle__ineq4) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  929 (all V_r_2 all V_ab_2 all V_x_2 all T_a (class_Rings_Olinordered__idom(T_a) -> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_ab_2)),V_r_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_r_2),V_x_2) & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_r_2))))) # label(fact_abs__diff__less__iff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  930 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))))) # label(fact_norm__triangle__ineq4) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  931 (all V_za_2 all V_w_2 (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_za_2))) # label(fact_zle__diff1__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  932 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c))))) # label(fact_mod__diff__cong) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  933 (all V_y all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m)) # label(fact_zdiff__zmod__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  934 (all V_m all V_y all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m)) # label(fact_zdiff__zmod__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  935 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  936 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c))) # label(fact_mod__diff__left__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  937 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__right__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  938 (all V_l_2 all V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) <-> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  939 (all V_db_2 all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2) -> (c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_db_2))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  940 (all V_b_2 all V_ab_2 all T_a (class_Groups_Ogroup__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) <-> V_ab_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  941 (all V_b_2 all V_ab_2 all T_a (class_Groups_Oab__group__add(T_a) -> (V_ab_2 = V_b_2 <-> c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  942 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  943 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  944 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_abs__minus__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  945 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zdiff__zmult__distrib2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  946 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zdiff__zmult__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  947 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)))) # label(fact_mult__left_Odiff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  948 (all V_b all V_a_H all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)))) # label(fact_mult_Odiff__left) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  949 (all V_y all V_x all V_xa all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)))) # label(fact_mult__right_Odiff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  950 (all V_b_H all V_b all V_a all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)))) # label(fact_mult_Odiff__right) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  951 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))) # label(fact_diff__divide__distrib) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  952 (all V_ya all V_y all V_x all T_a (class_RealVector_Oreal__normed__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)))) # label(fact_divide_Odiff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  953 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) # label(fact_norm__minus__commute) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  954 (all V_x all V_q all V_p all T_a (class_Rings_Ocomm__ring(T_a) -> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)))) # label(fact_poly__diff) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  955 (all V_db_2 all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Groups_Oab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2) -> (V_ab_2 = V_b_2 <-> V_ca_2 = V_db_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  956 (all V_q all V_b all V_p all V_a all T_a (class_Groups_Oab__group__add(T_a) -> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)))) # label(fact_diff__pCons) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  957 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_abs__triangle__ineq3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  958 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_abs__triangle__ineq2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  959 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))))) # label(fact_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  960 (all V_b all V_a all V_y all V_x all T_a (class_RealVector_Oreal__normed__algebra(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))))) # label(fact_mult_Oprod__diff__prod) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  961 (all V_b all V_a all V_y all V_x all T_a (class_Rings_Oring(T_a) -> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)))) # label(fact_mult__diff__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  962 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2) <-> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2) = V_db_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  963 (all V_db_2 all V_b_2 all V_ca_2 all V_e_2 all V_ab_2 all T_a (class_Rings_Oring(T_a) -> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2) <-> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.85  964 (all V_b_2 all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) <-> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  965 (all V_b_2 all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  966 (all V_db_2 all V_ca_2 all V_b_2 all V_ab_2 all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2) -> (c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) <-> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_db_2))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  967 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_norm__triangle__ineq2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  968 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  969 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  970 (all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))) # label(fact_norm__triangle__ineq3) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  971 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) # label(fact_zmult__div__cancel) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  972 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n))) # label(fact_zmod__zdiv__equality_H) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  973 (all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__normed__vector(T_a) -> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))) # label(fact_norm__diff__triangle__ineq) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  974 (all V_x all V_z all V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) -> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))))) # label(fact_incr__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  975 (all V_h all V_d all V_c all V_b all V_a all T_a (class_RealVector_Oreal__field(T_a) -> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h)),V_d)))) # label(fact_DERIV__mult__lemma) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  976 (all V_X_2 all V_M_2 all T_a all T_b (class_RealVector_Oreal__normed__vector(T_b) & class_Orderings_Oord(T_a) -> ((all B_n (c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) -> (all B_n (c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) -> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))))))) # label(fact_lemmaCauchy) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  977 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  978 (all T_2 all T_1 (class_Orderings_Opreorder(T_1) -> class_Orderings_Opreorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  979 (all T_2 all T_1 (class_Orderings_Oorder(T_1) -> class_Orderings_Oorder(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  980 (all T_2 all T_1 (class_Orderings_Oord(T_1) -> class_Orderings_Oord(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  981 (all T_1 (class_Rings_Oidom(T_1) -> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  982 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  983 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  984 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  985 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  986 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  987 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  988 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  989 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  990 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  991 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  992 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  993 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  994 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  995 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  996 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  997 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  998 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  999 (all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1) -> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1000 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1001 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1002 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1003 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1004 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1005 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1006 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__ring__abs) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1007 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ono__zero__divisors) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1008 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1009 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1010 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Olinordered__idom) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1011 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1012 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1013 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1014 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1015 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oab__group__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1016 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ozero__neq__one) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1017 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1018 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1019 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1020 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1021 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1022 (all T_1 (class_Groups_Ocomm__monoid__add(T_1) -> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1023 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.86  1024 (all T_1 (class_Groups_Oab__group__add(T_1) -> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1025 (all T_1 (class_Fields_Ofield(T_1) -> class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1026 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1027 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Ocomm__ring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1028 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oorder) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1029 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1030 (all T_1 (class_Rings_Ocomm__semiring__0(T_1) -> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1031 (all T_1 (class_Rings_Olinordered__idom(T_1) -> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Orderings_Oord) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1032 (all T_1 (class_Rings_Ocomm__ring__1(T_1) -> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1033 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Power_Opower(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Power_Opower) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1034 (all T_1 (class_Groups_Ozero(T_1) -> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Ozero) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1035 (all T_1 (class_Rings_Ocomm__ring(T_1) -> class_Rings_Oring(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1036 (all T_1 (class_Rings_Oidom(T_1) -> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Oidom) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1037 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Groups_Oone(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Groups_Oone) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1038 (all T_1 (class_Rings_Ocomm__semiring__1(T_1) -> class_Rings_Odvd(tc_Polynomial_Opoly(T_1)))) # label(arity_Polynomial__Opoly__Rings_Odvd) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1039 (all V_y_2 all V_x_2 (-hBOOL(c_fequal(V_x_2,V_y_2)) | V_x_2 = V_y_2)) # label(help_c__fequal__1) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  1040 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(c_fequal(V_x_2,V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause).  [assumption].
% 1.47/1.98  
% 1.47/1.98  ============================== end of process non-clausal formulas ===
% 1.47/1.98  
% 1.47/1.98  ============================== PROCESS INITIAL CLAUSES ===============
% 1.47/1.98  
% 1.47/1.98  ============================== PREDICATE ELIMINATION =================
% 1.47/1.98  1041 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom).  [assumption].
% 1.47/1.98  1042 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__triangle__ineq) # label(axiom).  [clausify(3)].
% 1.47/1.98  1043 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A)) # label(fact_norm__zero) # label(axiom).  [clausify(13)].
% 1.47/1.98  1044 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(A,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__eq__zero) # label(axiom).  [clausify(16)].
% 1.47/1.98  1045 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__eq__zero) # label(axiom).  [clausify(16)].
% 1.47/1.98  1046 -class_RealVector_Oreal__normed__vector(A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)) = c_RealVector_Onorm__class_Onorm(A,B) # label(fact_abs__norm__cancel) # label(axiom).  [clausify(18)].
% 1.47/1.98  1047 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_norm__le__zero__iff) # label(axiom).  [clausify(29)].
% 1.47/1.98  1048 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_norm__le__zero__iff) # label(axiom).  [clausify(29)].
% 1.47/1.98  1049 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_norm__ratiotest__lemma) # label(axiom).  [clausify(70)].
% 1.47/1.98  1050 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) # label(fact_norm__ge__zero) # label(axiom).  [clausify(97)].
% 1.47/1.98  1051 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) # label(fact_norm__not__less__zero) # label(axiom).  [clausify(275)].
% 1.47/1.98  1052 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__norm__iff) # label(axiom).  [clausify(306)].
% 1.47/1.98  1053 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__norm__iff) # label(axiom).  [clausify(306)].
% 1.47/1.98  1054 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,E)) # label(fact_norm__add__less) # label(axiom).  [clausify(310)].
% 1.47/1.98  1055 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f29(B,A)) # label(fact_Bseq__def) # label(axiom).  [clausify(704)].
% 1.47/1.98  1056 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),f29(B,A)) # label(fact_Bseq__def) # label(axiom).  [clausify(704)].
% 1.47/1.98  1057 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f30(B,A,C))),C) # label(fact_Bseq__def) # label(axiom).  [clausify(704)].
% 1.47/1.98  1058 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,f38(C,B,A))),B) | c_SEQ_OBseq(A,C) # label(fact_BseqI) # label(axiom).  [clausify(772)].
% 1.47/1.98  1059 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f39(B,A)) # label(fact_BseqD) # label(axiom).  [clausify(773)].
% 1.47/1.98  1060 -class_RealVector_Oreal__normed__vector(A) | -c_SEQ_OBseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),f39(B,A)) # label(fact_BseqD) # label(axiom).  [clausify(773)].
% 1.47/1.98  1061 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,f51(C,D,B,A)) | c_SEQ_OBseq(A,D) # label(fact_BseqI2_H) # label(axiom).  [clausify(809)].
% 1.47/1.98  1062 -class_RealVector_Oreal__normed__vector(A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,f51(C,B,D,A))),C) | c_SEQ_OBseq(A,B) # label(fact_BseqI2_H) # label(axiom).  [clausify(809)].
% 1.47/1.98  1063 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__triangle__ineq4) # label(axiom).  [clausify(930)].
% 1.47/1.98  1064 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_norm__minus__commute) # label(axiom).  [clausify(953)].
% 1.47/1.98  1065 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_norm__triangle__ineq2) # label(axiom).  [clausify(967)].
% 1.47/1.98  1066 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_norm__triangle__ineq3) # label(axiom).  [clausify(970)].
% 1.47/1.98  1067 -class_RealVector_Oreal__normed__vector(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E)))) # label(fact_norm__diff__triangle__ineq) # label(axiom).  [clausify(973)].
% 1.47/1.98  1068 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | c_Orderings_Oord__class_Oless__eq(B,C,f56(D,C,B,A)) | -c_Orderings_Oord__class_Oless__eq(B,C,E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(D,E)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(D,C)))) # label(fact_lemmaCauchy) # label(axiom).  [clausify(976)].
% 1.47/1.98  1069 -class_RealVector_Oreal__normed__vector(A) | -class_Orderings_Oord(B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,hAPP(C,D),hAPP(C,f56(C,D,B,A)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(B,D,E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,E)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,hAPP(C,D)))) # label(fact_lemmaCauchy) # label(axiom).  [clausify(976)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))).  [resolve(1041,a,1042,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1041,a,1043,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1041,a,1044,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1041,a,1045,a)].
% 1.47/1.98  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A).  [resolve(1041,a,1046,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1041,a,1047,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1041,a,1048,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1041,a,1049,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)).  [resolve(1041,a,1050,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1041,a,1051,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1041,a,1052,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1041,a,1053,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1041,a,1054,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f29(A,tc_RealDef_Oreal)).  [resolve(1041,a,1055,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B)),f29(A,tc_RealDef_Oreal)).  [resolve(1041,a,1056,a)].
% 1.47/1.98  Derived: c_SEQ_OBseq(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__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f30(A,tc_RealDef_Oreal,B))),B).  [resolve(1041,a,1057,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,f38(B,A,tc_RealDef_Oreal))),A) | c_SEQ_OBseq(tc_RealDef_Oreal,B).  [resolve(1041,a,1058,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f39(A,tc_RealDef_Oreal)).  [resolve(1041,a,1059,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_RealDef_Oreal,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,B)),f39(A,tc_RealDef_Oreal)).  [resolve(1041,a,1060,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f51(B,C,A,tc_RealDef_Oreal)) | c_SEQ_OBseq(tc_RealDef_Oreal,C).  [resolve(1041,a,1061,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(A,f51(B,A,C,tc_RealDef_Oreal))),B) | c_SEQ_OBseq(tc_RealDef_Oreal,A).  [resolve(1041,a,1062,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))).  [resolve(1041,a,1063,a)].
% 1.47/1.98  Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)).  [resolve(1041,a,1064,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))).  [resolve(1041,a,1065,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))).  [resolve(1041,a,1066,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)))).  [resolve(1041,a,1067,a)].
% 1.47/1.98  Derived: -class_Orderings_Oord(A) | c_Orderings_Oord__class_Oless__eq(A,B,f56(C,B,A,tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(C,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(C,B)))).  [resolve(1041,a,1068,a)].
% 1.47/1.98  Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(B,C),hAPP(B,f56(B,C,A,tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(B,C)))).  [resolve(1041,a,1069,a)].
% 1.47/1.98  1070 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom).  [assumption].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))).  [resolve(1070,a,1042,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).  [resolve(1070,a,1043,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A.  [resolve(1070,a,1044,a)].
% 1.47/1.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A.  [resolve(1070,a,1045,a)].
% 1.47/1.98  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A).  [resolve(1070,a,1046,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A.  [resolve(1070,a,1047,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A.  [resolve(1070,a,1048,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C))) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B.  [resolve(1070,a,1049,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)).  [resolve(1070,a,1050,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1070,a,1051,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A.  [resolve(1070,a,1052,a)].
% 1.47/1.98  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A.  [resolve(1070,a,1053,a)].
% 1.47/1.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1070,a,1054,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f29(A,tc_Complex_Ocomplex)).  [resolve(1070,a,1055,a)].
% 1.47/1.98  Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B)),f29(A,tc_Complex_Ocomplex)).  [resolve(1070,a,1056,a)].
% 1.47/1.98  Derived: c_SEQ_OBseq(tc_Complex_Ocomplex,A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f30(A,tc_Complex_Ocomplex,B))),B).  [resolve(1070,a,1057,a)].
% 1.47/1.99  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,f38(B,A,tc_Complex_Ocomplex))),A) | c_SEQ_OBseq(tc_Complex_Ocomplex,B).  [resolve(1070,a,1058,a)].
% 1.47/1.99  Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f39(A,tc_Complex_Ocomplex)).  [resolve(1070,a,1059,a)].
% 1.47/1.99  Derived: -c_SEQ_OBseq(tc_Complex_Ocomplex,A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,B)),f39(A,tc_Complex_Ocomplex)).  [resolve(1070,a,1060,a)].
% 1.47/1.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,f51(B,C,A,tc_Complex_Ocomplex)) | c_SEQ_OBseq(tc_Complex_Ocomplex,C).  [resolve(1070,a,1061,a)].
% 1.47/1.99  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(A,f51(B,A,C,tc_Complex_Ocomplex))),B) | c_SEQ_OBseq(tc_Complex_Ocomplex,A).  [resolve(1070,a,1062,a)].
% 1.47/1.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))).  [resolve(1070,a,1063,a)].
% 1.47/1.99  Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,A)).  [resolve(1070,a,1064,a)].
% 1.47/1.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B))).  [resolve(1070,a,1065,a)].
% 1.47/1.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B))).  [resolve(1070,a,1066,a)].
% 1.47/1.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)))).  [resolve(1070,a,1067,a)].
% 1.47/1.99  Derived: -class_Orderings_Oord(A) | c_Orderings_Oord__class_Oless__eq(A,B,f56(C,B,A,tc_Complex_Ocomplex)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(C,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(C,B)))).  [resolve(1070,a,1068,a)].
% 1.47/1.99  Derived: -class_Orderings_Oord(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(B,C),hAPP(B,f56(B,C,A,tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B,C)))).  [resolve(1070,a,1069,a)].
% 1.47/2.13  1071 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
% 1.47/2.13  1072 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))) # label(fact_norm__mult__ineq) # label(axiom).  [clausify(4)].
% 1.47/2.13  1073 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult_Oadd__right) # label(axiom).  [clausify(8)].
% 1.47/2.13  1074 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_mult__right_Oadd) # label(axiom).  [clausify(10)].
% 1.47/2.13  1075 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__right_Ozero) # label(axiom).  [clausify(19)].
% 1.47/2.13  1076 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult_Ozero__right) # label(axiom).  [clausify(20)].
% 1.47/2.13  1077 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__left_Ozero) # label(axiom).  [clausify(22)].
% 1.47/2.13  1078 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult_Ozero__left) # label(axiom).  [clausify(23)].
% 1.47/2.13  1079 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_mult__left_Oadd) # label(axiom).  [clausify(67)].
% 1.47/2.13  1080 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_mult_Oadd__left) # label(axiom).  [clausify(68)].
% 1.47/2.13  1081 -class_RealVector_Oreal__normed__algebra(A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E)) # label(fact_norm__mult__less) # label(axiom).  [clausify(307)].
% 1.47/2.13  1082 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f4(B,A)) # label(fact_mult__left_Opos__bounded) # label(axiom).  [clausify(325)].
% 1.47/2.13  1083 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f4(C,A))) # label(fact_mult__left_Opos__bounded) # label(axiom).  [clausify(325)].
% 1.47/2.13  1084 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f5(B,A)) # label(fact_mult__right_Opos__bounded) # label(axiom).  [clausify(326)].
% 1.47/2.13  1085 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),f5(B,A))) # label(fact_mult__right_Opos__bounded) # label(axiom).  [clausify(326)].
% 1.47/2.13  1086 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(A)) # label(fact_mult_Opos__bounded) # label(axiom).  [clausify(343)].
% 1.47/2.13  1087 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f7(A))) # label(fact_mult_Opos__bounded) # label(axiom).  [clausify(343)].
% 1.47/2.13  1088 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f12(A)) # label(fact_mult_Ononneg__bounded) # label(axiom).  [clausify(432)].
% 1.47/2.13  1089 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f12(A))) # label(fact_mult_Ononneg__bounded) # label(axiom).  [clausify(432)].
% 1.47/2.13  1090 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f13(B,A)) # label(fact_mult__left_Ononneg__bounded) # label(axiom).  [clausify(448)].
% 1.47/2.13  1091 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f13(C,A))) # label(fact_mult__left_Ononneg__bounded) # label(axiom).  [clausify(448)].
% 1.47/2.13  1092 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f14(B,A)) # label(fact_mult__right_Ononneg__bounded) # label(axiom).  [clausify(449)].
% 1.47/2.13  1093 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),f14(B,A))) # label(fact_mult__right_Ononneg__bounded) # label(axiom).  [clausify(449)].
% 1.47/2.13  1094 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),f16(C,A))) # label(fact_mult__left_Obounded) # label(axiom).  [clausify(451)].
% 1.47/2.13  1095 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),f17(A))) # label(fact_mult_Obounded) # label(axiom).  [clausify(452)].
% 1.47/2.13  1096 -class_RealVector_Oreal__normed__algebra(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),f18(B,A))) # label(fact_mult__right_Obounded) # label(axiom).  [clausify(453)].
% 1.47/2.14  1097 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),C) # label(fact_mult__left_Odiff) # label(axiom).  [clausify(947)].
% 1.47/2.14  1098 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),C) # label(fact_mult_Odiff__left) # label(axiom).  [clausify(948)].
% 1.47/2.14  1099 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult__right_Odiff) # label(axiom).  [clausify(949)].
% 1.47/2.14  1100 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)) # label(fact_mult_Odiff__right) # label(axiom).  [clausify(950)].
% 1.47/2.14  1101 -class_RealVector_Oreal__normed__algebra(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Ominus__class_Ominus(A,C,E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),c_Groups_Ominus__class_Ominus(A,C,E))) # label(fact_mult_Oprod__diff__prod) # label(axiom).  [clausify(960)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))).  [resolve(1071,a,1072,a)].
% 1.47/2.14  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)).  [resolve(1071,a,1073,a)].
% 1.47/2.14  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1071,a,1075,a)].
% 1.47/2.14  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A).  [resolve(1071,a,1077,a)].
% 1.47/2.14  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)),B).  [resolve(1071,a,1079,a)].
% 1.47/2.14  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1071,a,1081,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f4(A,tc_RealDef_Oreal)).  [resolve(1071,a,1082,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f4(B,tc_RealDef_Oreal))).  [resolve(1071,a,1083,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f5(A,tc_RealDef_Oreal)).  [resolve(1071,a,1084,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f5(A,tc_RealDef_Oreal))).  [resolve(1071,a,1085,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(tc_RealDef_Oreal)).  [resolve(1071,a,1086,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f7(tc_RealDef_Oreal))).  [resolve(1071,a,1087,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f12(tc_RealDef_Oreal)).  [resolve(1071,a,1088,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f12(tc_RealDef_Oreal))).  [resolve(1071,a,1089,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f13(A,tc_RealDef_Oreal)).  [resolve(1071,a,1090,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f13(B,tc_RealDef_Oreal))).  [resolve(1071,a,1091,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f14(A,tc_RealDef_Oreal)).  [resolve(1071,a,1092,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f14(A,tc_RealDef_Oreal))).  [resolve(1071,a,1093,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),f16(B,tc_RealDef_Oreal))).  [resolve(1071,a,1094,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B))),f17(tc_RealDef_Oreal))).  [resolve(1071,a,1095,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)),f18(A,tc_RealDef_Oreal))).  [resolve(1071,a,1096,a)].
% 1.47/2.14  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),B).  [resolve(1071,a,1097,a)].
% 1.47/2.14  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C)).  [resolve(1071,a,1099,a)].
% 1.47/2.14  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D))).  [resolve(1071,a,1101,a)].
% 1.47/2.14  1102 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))).  [resolve(1102,a,1072,a)].
% 1.47/2.14  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)).  [resolve(1102,a,1073,a)].
% 1.47/2.14  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).  [resolve(1102,a,1075,a)].
% 1.47/2.14  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A).  [resolve(1102,a,1077,a)].
% 1.47/2.14  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C)),B).  [resolve(1102,a,1079,a)].
% 1.47/2.14  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,C),D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1102,a,1081,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f4(A,tc_Complex_Ocomplex)).  [resolve(1102,a,1082,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f4(B,tc_Complex_Ocomplex))).  [resolve(1102,a,1083,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f5(A,tc_Complex_Ocomplex)).  [resolve(1102,a,1084,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f5(A,tc_Complex_Ocomplex))).  [resolve(1102,a,1085,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f7(tc_Complex_Ocomplex)).  [resolve(1102,a,1086,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f7(tc_Complex_Ocomplex))).  [resolve(1102,a,1087,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f12(tc_Complex_Ocomplex)).  [resolve(1102,a,1088,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f12(tc_Complex_Ocomplex))).  [resolve(1102,a,1089,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f13(A,tc_Complex_Ocomplex)).  [resolve(1102,a,1090,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f13(B,tc_Complex_Ocomplex))).  [resolve(1102,a,1091,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f14(A,tc_Complex_Ocomplex)).  [resolve(1102,a,1092,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f14(A,tc_Complex_Ocomplex))).  [resolve(1102,a,1093,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),f16(B,tc_Complex_Ocomplex))).  [resolve(1102,a,1094,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B))),f17(tc_Complex_Ocomplex))).  [resolve(1102,a,1095,a)].
% 1.47/2.14  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)),f18(A,tc_Complex_Ocomplex))).  [resolve(1102,a,1096,a)].
% 1.47/2.14  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),B).  [resolve(1102,a,1097,a)].
% 2.15/2.36  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,C)).  [resolve(1102,a,1099,a)].
% 2.15/2.36  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D))).  [resolve(1102,a,1101,a)].
% 2.15/2.36  1103 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom).  [assumption].
% 2.15/2.36  1104 -class_RealVector_Oreal__normed__div__algebra(A) | c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)) # label(fact_norm__mult) # label(axiom).  [clausify(7)].
% 2.15/2.36  1105 -class_RealVector_Oreal__normed__div__algebra(A) | c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C) # label(fact_norm__power) # label(axiom).  [clausify(536)].
% 2.15/2.36  Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)).  [resolve(1103,a,1104,a)].
% 2.15/2.36  Derived: c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B).  [resolve(1103,a,1105,a)].
% 2.15/2.36  1106 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom).  [assumption].
% 2.15/2.36  Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)).  [resolve(1106,a,1104,a)].
% 2.15/2.36  Derived: c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B).  [resolve(1106,a,1105,a)].
% 2.15/2.36  1107 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) # label(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [assumption].
% 2.15/2.36  1108 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom).  [clausify(11)].
% 2.15/2.36  1109 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_crossproduct__noteq) # label(axiom).  [clausify(11)].
% 2.15/2.36  1110 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)) # label(fact_crossproduct__noteq) # label(axiom).  [clausify(11)].
% 2.15/2.36  1111 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom).  [clausify(25)].
% 2.15/2.36  1112 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,B,C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom).  [clausify(25)].
% 2.15/2.36  1113 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C != D | E = F | c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) != c_Groups_Oplus__class_Oplus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)) # label(fact_add__scale__eq__noteq) # label(axiom).  [clausify(30)].
% 2.15/2.36  1114 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom).  [clausify(65)].
% 2.15/2.36  1115 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B != D # label(fact_crossproduct__eq) # label(axiom).  [clausify(65)].
% 2.15/2.36  1116 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | C != E # label(fact_crossproduct__eq) # label(axiom).  [clausify(65)].
% 2.15/2.36  Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)).  [resolve(1107,a,1108,a)].
% 2.15/2.36  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)).  [resolve(1107,a,1109,a)].
% 2.15/2.36  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)).  [resolve(1107,a,1110,a)].
% 2.15/2.36  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1107,a,1111,a)].
% 2.15/2.36  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1107,a,1112,a)].
% 2.15/2.37  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E)).  [resolve(1107,a,1113,a)].
% 2.15/2.37  1117 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [assumption].
% 2.15/2.37  Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1117,a,1108,a)].
% 2.15/2.37  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1117,a,1109,a)].
% 2.15/2.37  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),B)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),A)).  [resolve(1117,a,1110,a)].
% 2.15/2.37  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1117,a,1111,a)].
% 2.15/2.37  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(1117,a,1112,a)].
% 2.15/2.37  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E)).  [resolve(1117,a,1113,a)].
% 2.15/2.37  1118 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [assumption].
% 2.15/2.37  Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).  [resolve(1118,a,1108,a)].
% 2.15/2.37  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).  [resolve(1118,a,1109,a)].
% 2.15/2.37  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)).  [resolve(1118,a,1110,a)].
% 2.15/2.37  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1118,a,1111,a)].
% 2.15/2.37  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B.  [resolve(1118,a,1112,a)].
% 2.15/2.37  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),E)).  [resolve(1118,a,1113,a)].
% 2.15/2.38  1119 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [assumption].
% 2.15/2.38  Derived: A = B | C = D | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)).  [resolve(1119,a,1108,a)].
% 2.15/2.38  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)).  [resolve(1119,a,1109,a)].
% 2.15/2.38  Derived: A != B | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A)).  [resolve(1119,a,1110,a)].
% 2.15/2.38  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B.  [resolve(1119,a,1111,a)].
% 2.15/2.38  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B.  [resolve(1119,a,1112,a)].
% 2.15/2.38  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | B != C | D = E | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),E)).  [resolve(1119,a,1113,a)].
% 2.15/2.38  1120 -class_Rings_Oidom(A) | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom).  [clausify(981)].
% 2.15/2.38  Derived: -class_Rings_Oidom(A) | B = C | D = E | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1120,b,1108,a)].
% 2.15/2.38  Derived: -class_Rings_Oidom(A) | B != C | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1120,b,1109,a)].
% 2.15/2.38  Derived: -class_Rings_Oidom(A) | B != C | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B)).  [resolve(1120,b,1110,a)].
% 2.15/2.38  Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1120,b,1111,a)].
% 2.15/2.38  Derived: -class_Rings_Oidom(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1120,b,1112,a)].
% 2.25/2.48  Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | C != D | E = F | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),F)).  [resolve(1120,b,1113,a)].
% 2.25/2.48  1121 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom).  [assumption].
% 2.25/2.48  1122 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__le__cases) # label(axiom).  [clausify(31)].
% 2.25/2.48  1123 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__linear) # label(axiom).  [clausify(45)].
% 2.25/2.48  1124 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | B = C | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__cases) # label(axiom).  [clausify(167)].
% 2.25/2.48  1125 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neqE) # label(axiom).  [clausify(182)].
% 2.25/2.48  1126 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | B = C # label(fact_linorder__antisym__conv3) # label(axiom).  [clausify(183)].
% 2.25/2.48  1127 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) | B != C # label(fact_linorder__antisym__conv3) # label(axiom).  [clausify(183)].
% 2.25/2.48  1128 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | B = C | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__less__linear) # label(axiom).  [clausify(184)].
% 2.25/2.48  1129 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) | C = B # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(185)].
% 2.25/2.48  1130 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(185)].
% 2.25/2.48  1131 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_not__less__iff__gr__or__eq) # label(axiom).  [clausify(185)].
% 2.25/2.48  1132 -class_Orderings_Olinorder(A) | B = C | c_Orderings_Oord__class_Oless(A,C,B) | c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(186)].
% 2.25/2.48  1133 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(186)].
% 2.25/2.48  1134 -class_Orderings_Olinorder(A) | B != C | -c_Orderings_Oord__class_Oless(A,B,C) # label(fact_linorder__neq__iff) # label(axiom).  [clausify(186)].
% 2.25/2.48  1135 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,B,C) | C = B # label(fact_linorder__antisym__conv2) # label(axiom).  [clausify(195)].
% 2.25/2.48  1136 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,B,C) | C != B # label(fact_linorder__antisym__conv2) # label(axiom).  [clausify(195)].
% 2.25/2.48  1137 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_leD) # label(axiom).  [clausify(197)].
% 2.25/2.48  1138 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | C = B # label(fact_linorder__antisym__conv1) # label(axiom).  [clausify(200)].
% 2.25/2.48  1139 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,B,C) | C != B # label(fact_linorder__antisym__conv1) # label(axiom).  [clausify(200)].
% 2.25/2.48  1140 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_not__leE) # label(axiom).  [clausify(201)].
% 2.25/2.49  1141 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_leI) # label(axiom).  [clausify(202)].
% 2.25/2.49  1142 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__le__less__linear) # label(axiom).  [clausify(206)].
% 2.25/2.49  1143 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom).  [clausify(207)].
% 2.25/2.49  1144 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,C,B) # label(fact_linorder__not__le) # label(axiom).  [clausify(207)].
% 2.25/2.49  1145 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom).  [clausify(208)].
% 2.25/2.49  1146 -class_Orderings_Olinorder(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_linorder__not__less) # label(axiom).  [clausify(208)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,A).  [resolve(1121,a,1122,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | A = B | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).  [resolve(1121,a,1124,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A) | A != B.  [resolve(1121,a,1127,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).  [resolve(1121,a,1130,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B != A.  [resolve(1121,a,1131,a)].
% 2.25/2.49  Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).  [resolve(1121,a,1134,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | B = A.  [resolve(1121,a,1135,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).  [resolve(1121,a,1137,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | B != A.  [resolve(1121,a,1139,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).  [resolve(1121,a,1140,a)].
% 2.25/2.49  1147 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom).  [assumption].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,A).  [resolve(1147,a,1122,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | A = B | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).  [resolve(1147,a,1124,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A) | A != B.  [resolve(1147,a,1127,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).  [resolve(1147,a,1130,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B != A.  [resolve(1147,a,1131,a)].
% 2.25/2.49  Derived: A != B | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).  [resolve(1147,a,1134,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | B = A.  [resolve(1147,a,1135,a)].
% 2.25/2.49  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).  [resolve(1147,a,1137,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | B != A.  [resolve(1147,a,1139,a)].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).  [resolve(1147,a,1140,a)].
% 2.25/2.49  1148 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Orderings_Olinorder) # label(axiom).  [assumption].
% 2.25/2.49  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A).  [resolve(1148,a,1122,a)].
% 2.39/2.60  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | A = B | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A).  [resolve(1148,a,1124,a)].
% 2.39/2.60  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A) | A != B.  [resolve(1148,a,1127,a)].
% 2.39/2.60  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A).  [resolve(1148,a,1130,a)].
% 2.39/2.60  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B != A.  [resolve(1148,a,1131,a)].
% 2.39/2.60  Derived: A != B | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).  [resolve(1148,a,1134,a)].
% 2.39/2.60  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | B = A.  [resolve(1148,a,1135,a)].
% 2.39/2.60  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A).  [resolve(1148,a,1137,a)].
% 2.39/2.60  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | B != A.  [resolve(1148,a,1139,a)].
% 2.39/2.60  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,A).  [resolve(1148,a,1140,a)].
% 2.39/2.60  1149 -class_Rings_Olinordered__idom(A) | class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom).  [clausify(1019)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,B).  [resolve(1149,b,1122,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | B = C | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B).  [resolve(1149,b,1124,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B) | B != C.  [resolve(1149,b,1127,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B).  [resolve(1149,b,1130,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C != B.  [resolve(1149,b,1131,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | B != C | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C).  [resolve(1149,b,1134,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | C = B.  [resolve(1149,b,1135,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B).  [resolve(1149,b,1137,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | C != B.  [resolve(1149,b,1139,a)].
% 2.39/2.60  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,B).  [resolve(1149,b,1140,a)].
% 2.39/2.60  1150 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom).  [assumption].
% 2.39/2.60  1151 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom).  [clausify(71)].
% 2.39/2.60  1152 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom).  [clausify(71)].
% 2.39/2.61  1153 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom).  [clausify(71)].
% 2.39/2.61  1154 -class_Rings_Oordered__ring__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__eq__mult) # label(axiom).  [clausify(71)].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)).  [resolve(1150,a,1151,a)].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)).  [resolve(1150,a,1152,a)].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)).  [resolve(1150,a,1153,a)].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)).  [resolve(1150,a,1154,a)].
% 2.39/2.61  1155 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring__abs) # label(axiom).  [assumption].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)).  [resolve(1155,a,1151,a)].
% 2.39/2.61  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)).  [resolve(1155,a,1152,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)).  [resolve(1155,a,1153,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)).  [resolve(1155,a,1154,a)].
% 2.51/2.72  1156 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring__abs) # label(axiom).  [clausify(1006)].
% 2.51/2.72  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)).  [resolve(1156,b,1151,a)].
% 2.51/2.72  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)).  [resolve(1156,b,1152,a)].
% 2.51/2.72  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)).  [resolve(1156,b,1153,a)].
% 2.51/2.72  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)).  [resolve(1156,b,1154,a)].
% 2.51/2.72  1157 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
% 2.51/2.72  1158 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__le__zero__iff) # label(axiom).  [clausify(73)].
% 2.51/2.72  1159 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__le__zero__iff) # label(axiom).  [clausify(73)].
% 2.51/2.72  1160 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__le__zero__iff) # label(axiom).  [clausify(73)].
% 2.51/2.72  1161 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom).  [clausify(79)].
% 2.51/2.72  1162 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom).  [clausify(79)].
% 2.51/2.72  1163 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom).  [clausify(79)].
% 2.51/2.72  1164 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1165 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1166 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1167 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1168 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1169 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__mult__iff) # label(axiom).  [clausify(135)].
% 2.51/2.72  1170 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1171 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1172 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1173 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1174 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1175 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_mult__le__0__iff) # label(axiom).  [clausify(136)].
% 2.51/2.72  1176 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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)) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1177 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1178 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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)) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1179 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1180 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1181 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__right__disj) # label(axiom).  [clausify(244)].
% 2.51/2.72  1182 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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)) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1183 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1184 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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)) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1185 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1186 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1187 -class_Rings_Olinordered__ring__strict(A) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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) # label(fact_mult__less__cancel__left__disj) # label(axiom).  [clausify(245)].
% 2.51/2.72  1188 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom).  [clausify(246)].
% 2.51/2.72  1189 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__cancel__left__pos) # label(axiom).  [clausify(246)].
% 2.51/2.72  1190 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom).  [clausify(252)].
% 2.51/2.72  1191 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,D,C) # label(fact_mult__less__cancel__left__neg) # label(axiom).  [clausify(252)].
% 2.51/2.72  1192 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__neg__neg) # label(axiom).  [clausify(254)].
% 2.51/2.72  1193 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__strict__right__mono__neg) # label(axiom).  [clausify(258)].
% 2.51/2.72  1194 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_mult__strict__left__mono__neg) # label(axiom).  [clausify(259)].
% 2.51/2.72  1195 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom).  [clausify(296)].
% 2.51/2.72  1196 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,D,C) # label(fact_mult__le__cancel__left__neg) # label(axiom).  [clausify(296)].
% 2.51/2.72  1197 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom).  [clausify(297)].
% 2.51/2.72  1198 -class_Rings_Olinordered__ring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_mult__le__cancel__left__pos) # label(axiom).  [clausify(297)].
% 2.51/2.72  1199 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__gt__zero__iff) # label(axiom).  [clausify(304)].
% 2.51/2.72  1200 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__gt__zero__iff) # label(axiom).  [clausify(304)].
% 2.51/2.72  1201 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__gt__zero__iff) # label(axiom).  [clausify(304)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1157,a,1158,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1157,a,1159,a)].
% 2.51/2.72  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1157,a,1160,a)].
% 2.51/2.72  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1157,a,1161,a)].
% 2.51/2.72  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1157,a,1162,a)].
% 2.51/2.72  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1157,a,1163,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1165,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1166,a)].
% 2.51/2.72  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).  [resolve(1157,a,1168,a)].
% 2.51/2.72  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1169,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).  [resolve(1157,a,1171,a)].
% 2.51/2.72  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1172,a)].
% 2.51/2.72  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1174,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).  [resolve(1157,a,1175,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1176,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A).  [resolve(1157,a,1177,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1178,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A).  [resolve(1157,a,1179,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C).  [resolve(1157,a,1180,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A).  [resolve(1157,a,1181,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1182,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B).  [resolve(1157,a,1183,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1157,a,1184,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B).  [resolve(1157,a,1185,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).  [resolve(1157,a,1186,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B).  [resolve(1157,a,1187,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).  [resolve(1157,a,1188,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B).  [resolve(1157,a,1190,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).  [resolve(1157,a,1192,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B).  [resolve(1157,a,1195,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B).  [resolve(1157,a,1196,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C).  [resolve(1157,a,1197,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C).  [resolve(1157,a,1198,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1157,a,1199,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1157,a,1200,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1157,a,1201,a)].
% 2.51/2.73  1202 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring__strict) # label(axiom).  [assumption].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1202,a,1158,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1202,a,1159,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B.  [resolve(1202,a,1160,a)].
% 2.51/2.73  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1202,a,1161,a)].
% 2.51/2.73  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1202,a,1162,a)].
% 2.51/2.73  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(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.  [resolve(1202,a,1163,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1165,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1166,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1202,a,1168,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1169,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1202,a,1171,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1172,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1174,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1202,a,1175,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | 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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1176,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | 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,A).  [resolve(1202,a,1177,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1178,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A).  [resolve(1202,a,1179,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -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,A,C).  [resolve(1202,a,1180,a)].
% 2.51/2.73  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,A).  [resolve(1202,a,1181,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | 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_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1182,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | 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,B).  [resolve(1202,a,1183,a)].
% 2.51/2.73  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1202,a,1184,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B).  [resolve(1202,a,1185,a)].
% 2.51/2.74  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -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).  [resolve(1202,a,1186,a)].
% 2.51/2.74  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B).  [resolve(1202,a,1187,a)].
% 2.51/2.74  Derived: -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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).  [resolve(1202,a,1188,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B).  [resolve(1202,a,1190,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).  [resolve(1202,a,1192,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B).  [resolve(1202,a,1195,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B).  [resolve(1202,a,1196,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C).  [resolve(1202,a,1197,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C).  [resolve(1202,a,1198,a)].
% 2.51/2.74  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(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.  [resolve(1202,a,1199,a)].
% 2.51/2.74  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1202,a,1200,a)].
% 2.51/2.74  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1202,a,1201,a)].
% 2.51/2.74  1203 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) # label(axiom).  [clausify(994)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1203,b,1158,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1203,b,1159,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1203,b,1160,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1203,b,1161,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1203,b,1162,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1203,b,1163,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1165,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1166,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C).  [resolve(1203,b,1168,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1169,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C).  [resolve(1203,b,1171,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1172,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1174,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C).  [resolve(1203,b,1175,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1176,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B).  [resolve(1203,b,1177,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1178,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B).  [resolve(1203,b,1179,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D).  [resolve(1203,b,1180,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,B).  [resolve(1203,b,1181,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1182,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1183,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1203,b,1184,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1185,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D).  [resolve(1203,b,1186,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1187,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D).  [resolve(1203,b,1188,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1190,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1203,b,1192,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1195,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C).  [resolve(1203,b,1196,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D).  [resolve(1203,b,1197,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D).  [resolve(1203,b,1198,a)].
% 2.51/2.74  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1203,b,1199,a)].
% 2.66/2.86  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1203,b,1200,a)].
% 2.66/2.86  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1203,b,1201,a)].
% 2.66/2.86  1204 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom).  [assumption].
% 2.66/2.86  1205 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))) # label(fact_sum__squares__ge__zero) # label(axiom).  [clausify(74)].
% 2.66/2.86  1206 -class_Rings_Olinordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)) # label(fact_zero__le__square) # label(axiom).  [clausify(134)].
% 2.66/2.86  1207 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__square__less__zero) # label(axiom).  [clausify(243)].
% 2.66/2.86  1208 -class_Rings_Olinordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__sum__squares__lt__zero) # label(axiom).  [clausify(305)].
% 2.66/2.86  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))).  [resolve(1204,a,1205,a)].
% 2.66/2.86  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)).  [resolve(1204,a,1206,a)].
% 2.66/2.86  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1204,a,1207,a)].
% 2.66/2.86  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1204,a,1208,a)].
% 2.66/2.86  1209 class_Rings_Olinordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__ring) # label(axiom).  [assumption].
% 2.66/2.86  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))).  [resolve(1209,a,1205,a)].
% 2.66/2.86  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)).  [resolve(1209,a,1206,a)].
% 2.66/2.86  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1209,a,1207,a)].
% 2.66/2.86  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1209,a,1208,a)].
% 2.73/2.98  1210 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__ring) # label(axiom).  [clausify(1009)].
% 2.73/2.98  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C))).  [resolve(1210,b,1205,a)].
% 2.73/2.98  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)).  [resolve(1210,b,1206,a)].
% 2.73/2.98  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1210,b,1207,a)].
% 2.73/2.98  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1210,b,1208,a)].
% 2.73/2.98  1211 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom).  [assumption].
% 2.73/2.98  1212 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) # label(fact_abs__triangle__ineq) # label(axiom).  [clausify(75)].
% 2.73/2.98  1213 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__ge__zero) # label(axiom).  [clausify(76)].
% 2.73/2.98  1214 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__le__zero__iff) # label(axiom).  [clausify(77)].
% 2.73/2.98  1215 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__le__zero__iff) # label(axiom).  [clausify(77)].
% 2.73/2.98  1216 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__nonneg) # label(axiom).  [clausify(78)].
% 2.73/2.98  1217 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,B) # label(fact_abs__idempotent) # label(axiom).  [clausify(107)].
% 2.73/2.98  1218 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__eq__0) # label(axiom).  [clausify(127)].
% 2.73/2.98  1219 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__eq__0) # label(axiom).  [clausify(127)].
% 2.73/2.98  1220 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_abs__zero) # label(axiom).  [clausify(128)].
% 2.73/2.98  1221 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oabs__class_Oabs(A,B)) # label(fact_abs__ge__self) # label(axiom).  [clausify(129)].
% 2.73/2.98  1222 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,B),C) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_abs__le__D1) # label(axiom).  [clausify(130)].
% 2.73/2.98  1223 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) = c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)) # label(fact_abs__add__abs) # label(axiom).  [clausify(133)].
% 2.73/2.98  1224 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__not__less__zero) # label(axiom).  [clausify(268)].
% 2.73/2.98  1225 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__abs__iff) # label(axiom).  [clausify(269)].
% 2.73/2.98  1226 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__abs__iff) # label(axiom).  [clausify(269)].
% 2.73/2.98  1227 -class_Groups_Oordered__ab__group__add__abs(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Groups_Oabs__class_Oabs(A,B) = B # label(fact_abs__of__pos) # label(axiom).  [clausify(270)].
% 2.73/2.98  1228 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E)))) # label(fact_abs__diff__triangle__ineq) # label(axiom).  [clausify(927)].
% 2.73/2.98  1229 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))) # label(fact_abs__triangle__ineq4) # label(axiom).  [clausify(928)].
% 2.73/2.98  1230 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)) = c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)) # label(fact_abs__minus__commute) # label(axiom).  [clausify(944)].
% 2.73/2.98  1231 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_abs__triangle__ineq3) # label(axiom).  [clausify(957)].
% 2.73/2.98  1232 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))) # label(fact_abs__triangle__ineq2) # label(axiom).  [clausify(958)].
% 2.73/2.98  1233 -class_Groups_Oordered__ab__group__add__abs(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B))) # label(fact_abs__triangle__ineq2__sym) # label(axiom).  [clausify(959)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))).  [resolve(1211,a,1212,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)).  [resolve(1211,a,1213,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1211,a,1214,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A.  [resolve(1211,a,1215,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A.  [resolve(1211,a,1216,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,A).  [resolve(1211,a,1217,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1211,a,1218,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A.  [resolve(1211,a,1219,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1211,a,1220,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)).  [resolve(1211,a,1221,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).  [resolve(1211,a,1222,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)).  [resolve(1211,a,1223,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1211,a,1224,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A.  [resolve(1211,a,1225,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1211,a,1226,a)].
% 2.73/2.98  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Groups_Oabs__class_Oabs(tc_Int_Oint,A) = A.  [resolve(1211,a,1227,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,D)))).  [resolve(1211,a,1228,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))).  [resolve(1211,a,1229,a)].
% 2.73/2.98  Derived: c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B)) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A)).  [resolve(1211,a,1230,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B))),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B))).  [resolve(1211,a,1231,a)].
% 2.73/2.98  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B))).  [resolve(1211,a,1232,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,A))).  [resolve(1211,a,1233,a)].
% 2.73/2.99  1234 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) # label(axiom).  [assumption].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))).  [resolve(1234,a,1212,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)).  [resolve(1234,a,1213,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1234,a,1214,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1234,a,1215,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A.  [resolve(1234,a,1216,a)].
% 2.73/2.99  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A).  [resolve(1234,a,1217,a)].
% 2.73/2.99  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1234,a,1218,a)].
% 2.73/2.99  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1234,a,1219,a)].
% 2.73/2.99  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1234,a,1220,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)).  [resolve(1234,a,1221,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B).  [resolve(1234,a,1222,a)].
% 2.73/2.99  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)).  [resolve(1234,a,1223,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1234,a,1224,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1234,a,1225,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1234,a,1226,a)].
% 2.73/2.99  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A) = A.  [resolve(1234,a,1227,a)].
% 2.73/2.99  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,D))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)))).  [resolve(1234,a,1228,a)].
% 2.73/3.00  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))).  [resolve(1234,a,1229,a)].
% 2.73/3.00  Derived: c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A)).  [resolve(1234,a,1230,a)].
% 2.73/3.00  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))).  [resolve(1234,a,1231,a)].
% 2.73/3.00  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B))).  [resolve(1234,a,1232,a)].
% 2.73/3.00  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,A))).  [resolve(1234,a,1233,a)].
% 2.73/3.00  1235 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) # label(axiom).  [clausify(988)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))).  [resolve(1235,b,1212,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)).  [resolve(1235,b,1213,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1235,b,1214,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B.  [resolve(1235,b,1215,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) = B.  [resolve(1235,b,1216,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)) = c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B).  [resolve(1235,b,1217,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1235,b,1218,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B.  [resolve(1235,b,1219,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).  [resolve(1235,b,1220,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)).  [resolve(1235,b,1221,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C).  [resolve(1235,b,1222,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)).  [resolve(1235,b,1223,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1235,b,1224,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B.  [resolve(1235,b,1225,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1235,b,1226,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B) = B.  [resolve(1235,b,1227,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,E))),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,D)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,E)))).  [resolve(1235,b,1228,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))).  [resolve(1235,b,1229,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)) = c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,B)).  [resolve(1235,b,1230,a)].
% 2.73/3.00  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C))),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C))).  [resolve(1235,b,1231,a)].
% 2.87/3.12  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C))).  [resolve(1235,b,1232,a)].
% 2.87/3.12  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),C)),c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,B))).  [resolve(1235,b,1233,a)].
% 2.87/3.12  1236 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
% 2.87/3.12  1237 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_add__nonpos__nonpos) # label(axiom).  [clausify(80)].
% 2.87/3.12  1238 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)) # label(fact_add__nonneg__nonneg) # label(axiom).  [clausify(153)].
% 2.87/3.12  1239 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(154)].
% 2.87/3.12  1240 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(154)].
% 2.87/3.12  1241 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom).  [clausify(154)].
% 2.87/3.12  1242 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__increasing) # label(axiom).  [clausify(155)].
% 2.87/3.12  1243 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Oplus__class_Oplus(A,D,B)) # label(fact_add__increasing2) # label(axiom).  [clausify(156)].
% 2.87/3.12  1244 -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)) # label(fact_add__pos__pos) # label(axiom).  [clausify(262)].
% 2.87/3.12  1245 -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)) # label(fact_add__neg__neg) # label(axiom).  [clausify(264)].
% 2.87/3.12  1246 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_add__nonpos__neg) # label(axiom).  [clausify(298)].
% 2.87/3.12  1247 -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__eq(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)) # label(fact_add__neg__nonpos) # label(axiom).  [clausify(299)].
% 2.87/3.12  1248 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_add__strict__increasing2) # label(axiom).  [clausify(300)].
% 2.87/3.12  1249 -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__eq(A,C,D) | c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)) # label(fact_add__strict__increasing) # label(axiom).  [clausify(301)].
% 2.87/3.12  1250 -class_Groups_Oordered__comm__monoid__add(A) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_add__nonneg__pos) # label(axiom).  [clausify(302)].
% 2.87/3.12  1251 -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__eq(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)) # label(fact_add__pos__nonneg) # label(axiom).  [clausify(303)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1236,a,1237,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).  [resolve(1236,a,1238,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1236,a,1239,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1236,a,1240,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1236,a,1241,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)).  [resolve(1236,a,1242,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A)).  [resolve(1236,a,1243,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).  [resolve(1236,a,1244,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1236,a,1245,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1236,a,1246,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1236,a,1247,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)).  [resolve(1236,a,1248,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)).  [resolve(1236,a,1249,a)].
% 2.87/3.12  1252 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1252,a,1237,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)).  [resolve(1252,a,1238,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A.  [resolve(1252,a,1239,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1252,a,1240,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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.  [resolve(1252,a,1241,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).  [resolve(1252,a,1242,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)).  [resolve(1252,a,1243,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)).  [resolve(1252,a,1244,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1252,a,1245,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1252,a,1246,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1252,a,1247,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).  [resolve(1252,a,1248,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).  [resolve(1252,a,1249,a)].
% 2.87/3.12  1253 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) # label(axiom).  [assumption].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1253,a,1237,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)).  [resolve(1253,a,1238,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1253,a,1239,a)].
% 2.87/3.12  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1253,a,1240,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B.  [resolve(1253,a,1241,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)).  [resolve(1253,a,1242,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A)).  [resolve(1253,a,1243,a)].
% 2.87/3.13  Derived: -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),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)).  [resolve(1253,a,1244,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | 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)).  [resolve(1253,a,1245,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | 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)).  [resolve(1253,a,1246,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | 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)).  [resolve(1253,a,1247,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless__eq(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,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)).  [resolve(1253,a,1248,a)].
% 2.87/3.13  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)).  [resolve(1253,a,1249,a)].
% 2.87/3.13  1254 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) # label(axiom).  [clausify(989)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1254,b,1237,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)).  [resolve(1254,b,1238,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1254,b,1239,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1254,b,1240,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1254,b,1241,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)).  [resolve(1254,b,1242,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,B)).  [resolve(1254,b,1243,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)).  [resolve(1254,b,1244,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1254,b,1245,a)].
% 2.87/3.13  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1254,b,1246,a)].
% 3.05/3.27  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1254,b,1247,a)].
% 3.05/3.27  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)).  [resolve(1254,b,1248,a)].
% 3.05/3.27  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)).  [resolve(1254,b,1249,a)].
% 3.05/3.27  1255 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield__inverse__zero) # label(axiom).  [assumption].
% 3.05/3.27  1256 -class_Fields_Ofield__inverse__zero(A) | -class_RealVector_Oreal__normed__field(A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)) = c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_norm__divide) # label(axiom).  [clausify(81)].
% 3.05/3.27  1257 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(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)) # label(fact_add__num__frac) # label(axiom).  [clausify(157)].
% 3.05/3.27  1258 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(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) # label(fact_add__frac__num) # label(axiom).  [clausify(159)].
% 3.05/3.27  1259 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__left) # label(axiom).  [clausify(164)].
% 3.05/3.27  1260 -class_Fields_Ofield__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = c_Rings_Oinverse__class_Odivide(A,C,D) # label(fact_mult__divide__mult__cancel__right) # label(axiom).  [clausify(165)].
% 3.05/3.27  1261 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Odivide(A,B,D)),c_Rings_Oinverse__class_Odivide(A,C,E)) # label(fact_times__divide__times__eq) # label(axiom).  [clausify(311)].
% 3.05/3.27  1262 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) = B # label(fact_eq__divide__eq) # label(axiom).  [clausify(317)].
% 3.05/3.27  1263 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_eq__divide__eq) # label(axiom).  [clausify(317)].
% 3.05/3.27  1264 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom).  [clausify(317)].
% 3.05/3.27  1265 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_eq__divide__eq) # label(axiom).  [clausify(317)].
% 3.05/3.27  1266 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_eq__divide__eq) # label(axiom).  [clausify(317)].
% 3.05/3.27  1267 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) = B # label(fact_divide__eq__eq) # label(axiom).  [clausify(318)].
% 3.05/3.27  1268 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) != D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) = D # label(fact_divide__eq__eq) # label(axiom).  [clausify(318)].
% 3.05/3.27  1269 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | c_Groups_Ozero__class_Ozero(A) != C | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom).  [clausify(318)].
% 3.05/3.27  1270 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_divide__eq__eq) # label(axiom).  [clausify(318)].
% 3.05/3.27  1271 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,B,C) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) != B | c_Groups_Ozero__class_Ozero(A) != D # label(fact_divide__eq__eq) # label(axiom).  [clausify(318)].
% 3.05/3.27  1272 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Odivide(A,B,D)),C) # label(fact_power__divide) # label(axiom).  [clausify(567)].
% 3.05/3.27  1273 -class_Fields_Ofield__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Odivide(A,c_Groups_Oone__class_Oone(A),B)),C) # label(fact_power__one__over) # label(axiom).  [clausify(580)].
% 3.05/3.27  Derived: -class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B)) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1255,a,1256,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)).  [resolve(1255,a,1257,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C).  [resolve(1255,a,1258,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C).  [resolve(1255,a,1259,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C).  [resolve(1255,a,1260,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,D)).  [resolve(1255,a,1261,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) = A.  [resolve(1255,a,1262,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) != C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = C.  [resolve(1255,a,1263,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C.  [resolve(1255,a,1264,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1255,a,1265,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B) != A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != C.  [resolve(1255,a,1266,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)),B).  [resolve(1255,a,1272,a)].
% 3.05/3.27  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)),B).  [resolve(1255,a,1273,a)].
% 3.05/3.27  1274 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) # label(axiom).  [assumption].
% 3.05/3.27  Derived: -class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B)).  [resolve(1274,a,1256,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A)).  [resolve(1274,a,1257,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C).  [resolve(1274,a,1258,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C).  [resolve(1274,a,1259,a)].
% 3.05/3.27  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C).  [resolve(1274,a,1260,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C)),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,D)).  [resolve(1274,a,1261,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) = A.  [resolve(1274,a,1262,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) != C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = C.  [resolve(1274,a,1263,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C.  [resolve(1274,a,1264,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B.  [resolve(1274,a,1265,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B) != A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != C.  [resolve(1274,a,1266,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C)),B).  [resolve(1274,a,1272,a)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),A)),B).  [resolve(1274,a,1273,a)].
% 3.19/3.41  1275 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) # label(axiom).  [assumption].
% 3.19/3.41  1276 -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) # label(fact_divide__zero) # label(axiom).  [clausify(83)].
% 3.19/3.41  1277 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Rings_Oinverse__class_Odivide(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__self__if) # label(axiom).  [clausify(486)].
% 3.19/3.41  1278 -class_Rings_Odivision__ring__inverse__zero(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,B,B) # label(fact_divide__self__if) # label(axiom).  [clausify(486)].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1275,a,1276,a)].
% 3.19/3.41  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1275,a,1277,a)].
% 3.19/3.41  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,A).  [resolve(1275,a,1278,a)].
% 3.19/3.41  1279 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) # label(axiom).  [assumption].
% 3.19/3.41  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(1279,a,1276,a)].
% 3.19/3.41  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(1279,a,1277,a)].
% 3.34/3.54  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,A).  [resolve(1279,a,1278,a)].
% 3.34/3.54  1280 class_Rings_Odivision__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Odivision__ring) # label(axiom).  [assumption].
% 3.34/3.54  1281 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_divide__zero__left) # label(axiom).  [clausify(84)].
% 3.34/3.54  1282 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_times__divide__eq__right) # label(axiom).  [clausify(85)].
% 3.34/3.54  1283 -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)) # label(fact_add__divide__distrib) # label(axiom).  [clausify(86)].
% 3.34/3.54  1284 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_eq__divide__imp) # label(axiom).  [clausify(90)].
% 3.34/3.54  1285 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B) != D | c_Rings_Oinverse__class_Odivide(A,D,B) = C # label(fact_divide__eq__imp) # label(axiom).  [clausify(91)].
% 3.34/3.54  1286 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_nonzero__divide__eq__eq) # label(axiom).  [clausify(92)].
% 3.34/3.54  1287 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_nonzero__divide__eq__eq) # label(axiom).  [clausify(92)].
% 3.34/3.54  1288 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_nonzero__eq__divide__eq) # label(axiom).  [clausify(93)].
% 3.34/3.54  1289 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,C,B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_nonzero__eq__divide__eq) # label(axiom).  [clausify(93)].
% 3.34/3.54  1290 -class_Rings_Odivision__ring(A) | c_Rings_Oinverse__class_Odivide(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_divide__1) # label(axiom).  [clausify(462)].
% 3.34/3.54  1291 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) != c_Rings_Oinverse__class_Odivide(A,C,B) | C = B # label(fact_right__inverse__eq) # label(axiom).  [clausify(484)].
% 3.34/3.54  1292 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,C,B) | C != B # label(fact_right__inverse__eq) # label(axiom).  [clausify(484)].
% 3.34/3.54  1293 -class_Rings_Odivision__ring(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = c_Rings_Oinverse__class_Odivide(A,B,B) # label(fact_divide__self) # label(axiom).  [clausify(485)].
% 3.34/3.54  1294 -class_Rings_Odivision__ring(A) | c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Rings_Oinverse__class_Odivide(A,D,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_diff__divide__distrib) # label(axiom).  [clausify(951)].
% 3.34/3.54  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1280,a,1281,a)].
% 3.34/3.54  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1280,a,1282,a)].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1280,a,1283,a)].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A.  [resolve(1280,a,1290,a)].
% 3.43/3.67  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) | B = A.  [resolve(1280,a,1291,a)].
% 3.43/3.67  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A) | B != A.  [resolve(1280,a,1292,a)].
% 3.43/3.67  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C),B).  [resolve(1280,a,1294,a)].
% 3.43/3.67  1295 class_Rings_Odivision__ring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Odivision__ring) # label(axiom).  [assumption].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(1295,a,1281,a)].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)).  [resolve(1295,a,1282,a)].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,C),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,C)).  [resolve(1295,a,1283,a)].
% 3.43/3.67  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A.  [resolve(1295,a,1290,a)].
% 3.43/3.67  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) | B = A.  [resolve(1295,a,1291,a)].
% 3.43/3.67  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A) | B != A.  [resolve(1295,a,1292,a)].
% 3.43/3.67  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,A,B),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),B).  [resolve(1295,a,1294,a)].
% 3.43/3.67  1296 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
% 3.43/3.67  1297 -class_Groups_Oab__semigroup__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom).  [clausify(100)].
% 3.43/3.67  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)).  [resolve(1296,a,1297,a)].
% 3.43/3.67  1298 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
% 3.43/3.67  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1298,a,1297,a)].
% 3.74/3.94  1299 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
% 3.74/3.94  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).  [resolve(1299,a,1297,a)].
% 3.74/3.94  1300 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) # label(axiom).  [assumption].
% 3.74/3.94  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)).  [resolve(1300,a,1297,a)].
% 3.74/3.94  1301 -class_Rings_Ocomm__semiring__0(A) | class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) # label(axiom).  [clausify(1002)].
% 3.74/3.94  Derived: -class_Rings_Ocomm__semiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1301,b,1297,a)].
% 3.74/3.94  1302 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.94  1303 -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)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom).  [clausify(101)].
% 3.74/3.94  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)).  [resolve(1302,a,1303,a)].
% 3.74/3.94  1304 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.94  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).  [resolve(1304,a,1303,a)].
% 3.74/3.94  1305 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.94  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C)).  [resolve(1305,a,1303,a)].
% 3.74/3.94  1306 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.94  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,C)).  [resolve(1306,a,1303,a)].
% 3.74/3.94  1307 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oab__semigroup__add) # label(axiom).  [clausify(1004)].
% 3.74/3.94  Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,D)).  [resolve(1307,b,1303,a)].
% 3.74/3.94  1308 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.94  1309 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__cancel) # label(axiom).  [clausify(102)].
% 3.74/3.95  1310 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,B,D) | C != D # label(fact_add__left__cancel) # label(axiom).  [clausify(102)].
% 3.74/3.95  1311 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__cancel) # label(axiom).  [clausify(103)].
% 3.74/3.95  1312 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) = c_Groups_Oplus__class_Oplus(A,D,C) | B != D # label(fact_add__right__cancel) # label(axiom).  [clausify(103)].
% 3.74/3.95  1313 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,B,D) | C = D # label(fact_add__left__imp__eq) # label(axiom).  [clausify(104)].
% 3.74/3.95  1314 -class_Groups_Ocancel__semigroup__add(A) | c_Groups_Oplus__class_Oplus(A,B,C) != c_Groups_Oplus__class_Oplus(A,D,C) | B = D # label(fact_add__right__imp__eq) # label(axiom).  [clausify(106)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B = C.  [resolve(1308,a,1309,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C) | B != C.  [resolve(1308,a,1310,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A = C.  [resolve(1308,a,1311,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B) | A != C.  [resolve(1308,a,1312,a)].
% 3.74/3.95  1315 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B = C.  [resolve(1315,a,1309,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C) | B != C.  [resolve(1315,a,1310,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A = C.  [resolve(1315,a,1311,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B) | A != C.  [resolve(1315,a,1312,a)].
% 3.74/3.95  1316 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B = C.  [resolve(1316,a,1309,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C) | B != C.  [resolve(1316,a,1310,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A = C.  [resolve(1316,a,1311,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B) | A != C.  [resolve(1316,a,1312,a)].
% 3.74/3.95  1317 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B = C.  [resolve(1317,a,1309,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,C) | B != C.  [resolve(1317,a,1310,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A = C.  [resolve(1317,a,1311,a)].
% 3.74/3.95  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,B) | A != C.  [resolve(1317,a,1312,a)].
% 3.74/3.95  1318 -class_Groups_Ocancel__comm__monoid__add(A) | class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) # label(axiom).  [clausify(999)].
% 3.74/3.95  Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C = D.  [resolve(1318,b,1309,a)].
% 3.96/4.20  Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D) | C != D.  [resolve(1318,b,1310,a)].
% 3.96/4.20  Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B = D.  [resolve(1318,b,1311,a)].
% 3.96/4.20  Derived: -class_Groups_Ocancel__comm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C) | B != D.  [resolve(1318,b,1312,a)].
% 3.96/4.20  1319 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.96/4.20  1320 -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 # label(fact_add__imp__eq) # label(axiom).  [clausify(105)].
% 3.96/4.20  1321 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.96/4.20  1322 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.96/4.20  1323 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.96/4.20  1324 -class_Groups_Ocancel__comm__monoid__add(A) | class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) # label(axiom).  [clausify(991)].
% 3.96/4.20  1325 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom).  [assumption].
% 3.96/4.20  1326 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__zero__left) # label(axiom).  [clausify(108)].
% 3.96/4.20  1327 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__zero__right) # label(axiom).  [clausify(109)].
% 3.96/4.20  1328 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff) # label(axiom).  [clausify(575)].
% 3.96/4.20  1329 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C # label(fact_power__eq__0__iff) # label(axiom).  [clausify(575)].
% 3.96/4.20  1330 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C # label(fact_power__eq__0__iff) # label(axiom).  [clausify(575)].
% 3.96/4.20  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A).  [resolve(1325,a,1326,a)].
% 3.96/4.20  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1325,a,1327,a)].
% 3.96/4.20  Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1325,a,1328,b)].
% 3.96/4.20  Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(1325,a,1329,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1325,a,1330,b)].
% 3.96/4.21  1331 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom).  [assumption].
% 3.96/4.21  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A).  [resolve(1331,a,1326,a)].
% 3.96/4.21  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1331,a,1327,a)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A.  [resolve(1331,a,1328,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(1331,a,1329,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1331,a,1330,b)].
% 3.96/4.21  1332 class_Rings_Omult__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Omult__zero) # label(axiom).  [assumption].
% 3.96/4.21  Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1332,a,1328,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(1332,a,1329,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_RealDef_Oreal) | -class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Rings_Ozero__neq__one(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1332,a,1330,b)].
% 3.96/4.21  1333 class_Rings_Omult__zero(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Omult__zero) # label(axiom).  [assumption].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A.  [resolve(1333,a,1328,b)].
% 3.96/4.21  Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B.  [resolve(1333,a,1329,b)].
% 4.15/4.35  Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B.  [resolve(1333,a,1330,b)].
% 4.15/4.35  1334 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Omult__zero(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Omult__zero) # label(axiom).  [clausify(1026)].
% 4.15/4.35  Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B).  [resolve(1334,b,1326,a)].
% 4.15/4.35  Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1334,b,1327,a)].
% 4.15/4.35  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1334,b,1328,b)].
% 4.15/4.35  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C.  [resolve(1334,b,1329,b)].
% 4.15/4.35  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | -class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C.  [resolve(1334,b,1330,b)].
% 4.15/4.35  1335 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 4.15/4.35  1336 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom).  [clausify(110)].
% 4.15/4.35  1337 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom).  [clausify(110)].
% 4.15/4.35  1338 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom).  [clausify(110)].
% 4.15/4.35  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B.  [resolve(1335,a,1336,a)].
% 4.15/4.35  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A.  [resolve(1335,a,1337,a)].
% 4.15/4.35  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B.  [resolve(1335,a,1338,a)].
% 4.15/4.35  1339 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 4.15/4.35  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B.  [resolve(1339,a,1336,a)].
% 4.27/4.49  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1339,a,1337,a)].
% 4.27/4.49  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != B.  [resolve(1339,a,1338,a)].
% 4.27/4.49  1340 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 4.27/4.49  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B.  [resolve(1340,a,1336,a)].
% 4.27/4.49  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != A.  [resolve(1340,a,1337,a)].
% 4.27/4.49  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != B.  [resolve(1340,a,1338,a)].
% 4.27/4.49  1341 -class_Rings_Oidom(A) | class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) # label(axiom).  [clausify(995)].
% 4.27/4.49  Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C.  [resolve(1341,b,1336,a)].
% 4.27/4.49  Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B.  [resolve(1341,b,1337,a)].
% 4.27/4.49  Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != C.  [resolve(1341,b,1338,a)].
% 4.27/4.49  1342 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom).  [assumption].
% 4.27/4.49  1343 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B) = B # label(fact_add__0__left) # label(axiom).  [clausify(113)].
% 4.27/4.49  1344 -class_Groups_Omonoid__add(A) | c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom).  [clausify(116)].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A.  [resolve(1342,a,1343,a)].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A.  [resolve(1342,a,1344,a)].
% 4.27/4.49  1345 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom).  [assumption].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = A.  [resolve(1345,a,1343,a)].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A.  [resolve(1345,a,1344,a)].
% 4.27/4.49  1346 class_Groups_Omonoid__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__add) # label(axiom).  [assumption].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) = A.  [resolve(1346,a,1343,a)].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A.  [resolve(1346,a,1344,a)].
% 4.27/4.49  1347 class_Groups_Omonoid__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__add) # label(axiom).  [assumption].
% 4.27/4.49  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),A) = A.  [resolve(1347,a,1343,a)].
% 4.37/4.62  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A.  [resolve(1347,a,1344,a)].
% 4.37/4.62  1348 -class_Groups_Ocomm__monoid__add(A) | class_Groups_Omonoid__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__add) # label(axiom).  [clausify(1022)].
% 4.37/4.62  Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) = B.  [resolve(1348,b,1343,a)].
% 4.37/4.62  Derived: -class_Groups_Ocomm__monoid__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B.  [resolve(1348,b,1344,a)].
% 4.37/4.62  1349 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
% 4.37/4.62  1350 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom).  [clausify(115)].
% 4.37/4.62  1351 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom).  [clausify(115)].
% 4.37/4.62  1352 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(151)].
% 4.37/4.62  1353 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom).  [clausify(151)].
% 4.37/4.62  1354 -class_Groups_Olinordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(152)].
% 4.37/4.62  1355 -class_Groups_Olinordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom).  [clausify(152)].
% 4.37/4.62  1356 -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) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(260)].
% 4.37/4.62  1357 -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) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom).  [clausify(260)].
% 4.37/4.62  1358 -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)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(261)].
% 4.37/4.62  1359 -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)) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom).  [clausify(261)].
% 4.37/4.62  1360 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom).  [clausify(339)].
% 4.43/4.63  1361 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = c_Groups_Oplus__class_Oplus(A,B,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom).  [clausify(339)].
% 4.43/4.63  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A.  [resolve(1349,a,1350,a)].
% 4.43/4.63  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A.  [resolve(1349,a,1351,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).  [resolve(1349,a,1352,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1349,a,1354,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).  [resolve(1349,a,1356,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(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)).  [resolve(1349,a,1358,a)].
% 4.43/4.63  1362 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) # label(axiom).  [assumption].
% 4.43/4.63  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(1362,a,1350,a)].
% 4.43/4.63  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A) | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != A.  [resolve(1362,a,1351,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).  [resolve(1362,a,1352,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1362,a,1354,a)].
% 4.43/4.63  Derived: -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,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A).  [resolve(1362,a,1356,a)].
% 4.43/4.63  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,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)).  [resolve(1362,a,1358,a)].
% 4.43/4.63  1363 -class_Rings_Olinordered__idom(A) | class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) # label(axiom).  [clausify(990)].
% 4.43/4.63  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B.  [resolve(1363,b,1350,a)].
% 4.43/4.63  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B.  [resolve(1363,b,1351,a)].
% 4.43/4.63  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B).  [resolve(1363,b,1352,a)].
% 4.54/4.76  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1363,b,1354,a)].
% 4.54/4.76  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B).  [resolve(1363,b,1356,a)].
% 4.54/4.76  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1363,b,1358,a)].
% 4.54/4.76  1364 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 4.54/4.76  1365 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom).  [clausify(118)].
% 4.54/4.76  1366 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__cancel__right) # label(axiom).  [clausify(118)].
% 4.54/4.76  1367 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom).  [clausify(119)].
% 4.54/4.76  1368 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | -c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__cancel__left) # label(axiom).  [clausify(119)].
% 4.54/4.76  1369 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C)) | c_Orderings_Oord__class_Oless__eq(A,B,D) # label(fact_add__le__imp__le__right) # label(axiom).  [clausify(123)].
% 4.54/4.76  1370 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D)) | c_Orderings_Oord__class_Oless__eq(A,C,D) # label(fact_add__le__imp__le__left) # label(axiom).  [clausify(124)].
% 4.54/4.76  1371 -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) # label(fact_add__less__imp__less__left) # label(axiom).  [clausify(209)].
% 4.54/4.76  1372 -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) # label(fact_add__less__imp__less__right) # label(axiom).  [clausify(210)].
% 4.54/4.76  1373 -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) # label(fact_add__less__cancel__left) # label(axiom).  [clausify(214)].
% 4.54/4.76  1374 -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) # label(fact_add__less__cancel__left) # label(axiom).  [clausify(214)].
% 4.54/4.76  1375 -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) # label(fact_add__less__cancel__right) # label(axiom).  [clausify(215)].
% 4.54/4.76  1376 -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) # label(fact_add__less__cancel__right) # label(axiom).  [clausify(215)].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C).  [resolve(1364,a,1365,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C).  [resolve(1364,a,1366,a)].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C).  [resolve(1364,a,1367,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B,C).  [resolve(1364,a,1368,a)].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).  [resolve(1364,a,1371,a)].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C).  [resolve(1364,a,1372,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).  [resolve(1364,a,1374,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C).  [resolve(1364,a,1376,a)].
% 4.54/4.76  1377 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C).  [resolve(1377,a,1365,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C).  [resolve(1377,a,1366,a)].
% 4.54/4.76  Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,B,C).  [resolve(1377,a,1367,a)].
% 4.54/4.76  Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_Nat_Onat,B,C).  [resolve(1377,a,1368,a)].
% 4.54/4.76  Derived: -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).  [resolve(1377,a,1371,a)].
% 4.54/4.76  Derived: -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,C,B)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).  [resolve(1377,a,1372,a)].
% 4.57/4.77  Derived: 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).  [resolve(1377,a,1374,a)].
% 4.57/4.77  Derived: 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,C,B)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).  [resolve(1377,a,1376,a)].
% 4.57/4.77  1378 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 4.57/4.77  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C).  [resolve(1378,a,1365,a)].
% 4.57/4.77  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C).  [resolve(1378,a,1366,a)].
% 4.57/4.77  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C).  [resolve(1378,a,1367,a)].
% 4.57/4.77  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,C).  [resolve(1378,a,1368,a)].
% 4.57/4.77  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).  [resolve(1378,a,1371,a)].
% 4.57/4.77  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C).  [resolve(1378,a,1372,a)].
% 4.57/4.77  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).  [resolve(1378,a,1374,a)].
% 4.57/4.77  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C).  [resolve(1378,a,1376,a)].
% 4.57/4.77  1379 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom).  [clausify(983)].
% 4.57/4.77  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D).  [resolve(1379,b,1365,a)].
% 4.57/4.77  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D).  [resolve(1379,b,1366,a)].
% 4.57/4.77  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D).  [resolve(1379,b,1367,a)].
% 4.57/4.77  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),C,D).  [resolve(1379,b,1368,a)].
% 4.57/4.77  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D).  [resolve(1379,b,1371,a)].
% 4.78/5.05  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D).  [resolve(1379,b,1372,a)].
% 4.78/5.05  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D).  [resolve(1379,b,1374,a)].
% 4.78/5.05  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D).  [resolve(1379,b,1376,a)].
% 4.78/5.05  1380 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
% 4.78/5.05  1381 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)) # label(fact_add__right__mono) # label(axiom).  [clausify(120)].
% 4.78/5.05  1382 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)) # label(fact_add__left__mono) # label(axiom).  [clausify(121)].
% 4.78/5.05  1383 -class_Groups_Oordered__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)) # label(fact_add__mono) # label(axiom).  [clausify(122)].
% 4.78/5.05  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)).  [resolve(1380,a,1383,a)].
% 4.78/5.05  1384 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
% 4.78/5.05  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).  [resolve(1384,a,1383,a)].
% 4.78/5.05  1385 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) # label(axiom).  [assumption].
% 4.78/5.05  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1385,a,1383,a)].
% 4.78/5.05  1386 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) # label(axiom).  [clausify(987)].
% 4.78/5.05  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)).  [resolve(1386,b,1383,a)].
% 4.78/5.05  1387 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom).  [assumption].
% 4.78/5.05  1388 -class_Rings_Ocomm__semiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,D)),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom).  [clausify(125)].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)),B).  [resolve(1387,a,1388,a)].
% 4.95/5.18  1389 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom).  [assumption].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)),B).  [resolve(1389,a,1388,a)].
% 4.95/5.18  1390 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Ocomm__semiring) # label(axiom).  [assumption].
% 4.95/5.18  1391 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Ocomm__semiring) # label(axiom).  [assumption].
% 4.95/5.18  1392 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Ocomm__semiring) # label(axiom).  [clausify(1014)].
% 4.95/5.18  Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)),C).  [resolve(1392,b,1388,a)].
% 4.95/5.18  1393 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom).  [assumption].
% 4.95/5.18  1394 -class_Rings_Osemiring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D),E) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),E)) # label(fact_combine__common__factor) # label(axiom).  [clausify(126)].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),D)).  [resolve(1393,a,1394,a)].
% 4.95/5.18  1395 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom).  [assumption].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D)).  [resolve(1395,a,1394,a)].
% 4.95/5.18  1396 class_Rings_Osemiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring) # label(axiom).  [assumption].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),D)).  [resolve(1396,a,1394,a)].
% 4.95/5.18  1397 class_Rings_Osemiring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring) # label(axiom).  [assumption].
% 4.95/5.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B)),C),D) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),D)).  [resolve(1397,a,1394,a)].
% 5.08/5.31  1398 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring) # label(axiom).  [clausify(1030)].
% 5.08/5.31  Derived: -class_Rings_Ocomm__semiring__0(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),D),E) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),E)).  [resolve(1398,b,1394,a)].
% 5.08/5.31  1399 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
% 5.08/5.31  1400 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__nonneg__nonneg) # label(axiom).  [clausify(137)].
% 5.08/5.31  1401 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos) # label(axiom).  [clausify(138)].
% 5.08/5.31  1402 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonneg__nonpos2) # label(axiom).  [clausify(139)].
% 5.08/5.31  1403 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__nonpos__nonneg) # label(axiom).  [clausify(140)].
% 5.08/5.31  1404 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom).  [clausify(150)].
% 5.08/5.31  1405 -class_Rings_Oordered__cancel__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_split__mult__neg__le) # label(axiom).  [clausify(150)].
% 5.08/5.31  1406 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
% 5.08/5.31  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)).  [resolve(1406,a,1400,a)].
% 5.08/5.31  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1406,a,1401,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1406,a,1402,a)].
% 5.22/5.44  1407 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) # label(axiom).  [assumption].
% 5.22/5.44  1408 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) # label(axiom).  [clausify(993)].
% 5.22/5.44  1409 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom).  [assumption].
% 5.22/5.44  1410 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__nonpos__nonpos) # label(axiom).  [clausify(141)].
% 5.22/5.44  1411 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_mult__right__mono__neg) # label(axiom).  [clausify(145)].
% 5.22/5.44  1412 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_mult__left__mono__neg) # label(axiom).  [clausify(146)].
% 5.22/5.44  1413 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_split__mult__pos__le) # label(axiom).  [clausify(149)].
% 5.22/5.44  1414 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_split__mult__pos__le) # label(axiom).  [clausify(149)].
% 5.22/5.44  1415 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F) # label(fact_le__add__iff1) # label(axiom).  [clausify(919)].
% 5.22/5.44  1416 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F) # label(fact_le__add__iff1) # label(axiom).  [clausify(919)].
% 5.22/5.44  1417 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)) # label(fact_le__add__iff2) # label(axiom).  [clausify(920)].
% 5.22/5.44  1418 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)) # label(fact_le__add__iff2) # label(axiom).  [clausify(920)].
% 5.22/5.44  1419 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F) # label(fact_less__add__iff1) # label(axiom).  [clausify(921)].
% 5.22/5.44  1420 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F) # label(fact_less__add__iff1) # label(axiom).  [clausify(921)].
% 5.22/5.44  1421 -class_Rings_Oordered__ring(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)) # label(fact_less__add__iff2) # label(axiom).  [clausify(922)].
% 5.22/5.44  1422 -class_Rings_Oordered__ring(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)) # label(fact_less__add__iff2) # label(axiom).  [clausify(922)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)).  [resolve(1409,a,1411,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)).  [resolve(1409,a,1412,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C),E).  [resolve(1409,a,1415,a)].
% 5.22/5.44  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C),E).  [resolve(1409,a,1416,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E)).  [resolve(1409,a,1417,a)].
% 5.22/5.44  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E)).  [resolve(1409,a,1418,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C),E).  [resolve(1409,a,1419,a)].
% 5.22/5.44  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C),E).  [resolve(1409,a,1420,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E)).  [resolve(1409,a,1421,a)].
% 5.22/5.44  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E)).  [resolve(1409,a,1422,a)].
% 5.22/5.44  1423 class_Rings_Oordered__ring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__ring) # label(axiom).  [assumption].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)).  [resolve(1423,a,1411,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)).  [resolve(1423,a,1412,a)].
% 5.22/5.44  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C),E).  [resolve(1423,a,1415,a)].
% 5.22/5.45  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C),E).  [resolve(1423,a,1416,a)].
% 5.22/5.45  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E)).  [resolve(1423,a,1417,a)].
% 5.22/5.45  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E)).  [resolve(1423,a,1418,a)].
% 5.22/5.45  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C),E).  [resolve(1423,a,1419,a)].
% 5.22/5.45  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C),E).  [resolve(1423,a,1420,a)].
% 5.22/5.45  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E)).  [resolve(1423,a,1421,a)].
% 5.22/5.45  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E)).  [resolve(1423,a,1422,a)].
% 5.22/5.45  1424 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__ring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__ring) # label(axiom).  [clausify(1017)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)).  [resolve(1424,b,1411,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B)).  [resolve(1424,b,1412,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D),F).  [resolve(1424,b,1415,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D),F).  [resolve(1424,b,1416,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F)).  [resolve(1424,b,1417,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F)).  [resolve(1424,b,1418,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D),F).  [resolve(1424,b,1419,a)].
% 5.22/5.45  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D),F).  [resolve(1424,b,1420,a)].
% 5.35/5.58  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F)).  [resolve(1424,b,1421,a)].
% 5.35/5.58  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F)).  [resolve(1424,b,1422,a)].
% 5.35/5.58  1425 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom).  [assumption].
% 5.35/5.58  1426 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__right__mono) # label(axiom).  [clausify(142)].
% 5.35/5.58  1427 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_mult__left__mono) # label(axiom).  [clausify(143)].
% 5.35/5.58  1428 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__mono_H) # label(axiom).  [clausify(147)].
% 5.35/5.58  1429 -class_Rings_Oordered__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__mono) # label(axiom).  [clausify(148)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)).  [resolve(1425,a,1426,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)).  [resolve(1425,a,1427,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1425,a,1428,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1425,a,1429,a)].
% 5.35/5.58  1430 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom).  [assumption].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1430,a,1426,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)).  [resolve(1430,a,1427,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1430,a,1428,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1430,a,1429,a)].
% 5.35/5.58  1431 class_Rings_Oordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__semiring) # label(axiom).  [assumption].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).  [resolve(1431,a,1426,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)).  [resolve(1431,a,1427,a)].
% 5.35/5.58  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1431,a,1428,a)].
% 5.51/5.71  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1431,a,1429,a)].
% 5.51/5.71  1432 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__semiring) # label(axiom).  [clausify(1005)].
% 5.51/5.71  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1432,b,1426,a)].
% 5.51/5.71  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)).  [resolve(1432,b,1427,a)].
% 5.51/5.71  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1432,b,1428,a)].
% 5.51/5.71  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1432,b,1429,a)].
% 5.51/5.71  1433 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom).  [assumption].
% 5.51/5.71  1434 -class_Rings_Oordered__comm__semiring(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_comm__mult__left__mono) # label(axiom).  [clausify(144)].
% 5.51/5.71  1435 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom).  [assumption].
% 5.51/5.71  1436 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oordered__comm__semiring) # label(axiom).  [assumption].
% 5.51/5.71  1437 -class_Rings_Olinordered__idom(A) | class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) # label(axiom).  [clausify(996)].
% 5.55/5.84  1438 class_Fields_Ofield(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Ofield) # label(axiom).  [assumption].
% 5.55/5.84  1439 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(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)) # label(fact_add__divide__eq__iff) # label(axiom).  [clausify(158)].
% 5.55/5.84  1440 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(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) # label(fact_divide__add__eq__iff) # label(axiom).  [clausify(160)].
% 5.55/5.84  1441 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(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)) # label(fact_add__frac__eq) # label(axiom).  [clausify(161)].
% 5.55/5.84  1442 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) != c_Rings_Oinverse__class_Odivide(A,E,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C) # label(fact_frac__eq__eq) # label(axiom).  [clausify(163)].
% 5.55/5.84  1443 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Rings_Oinverse__class_Odivide(A,D,C) = c_Rings_Oinverse__class_Odivide(A,E,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C) # label(fact_frac__eq__eq) # label(axiom).  [clausify(163)].
% 5.55/5.84  1444 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Odivide(A,C,B)),D) # label(fact_nonzero__power__divide) # label(axiom).  [clausify(577)].
% 5.55/5.84  1445 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,C),D) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)) # label(fact_poly__div__mult__right) # label(axiom).  [clausify(705)].
% 5.55/5.84  1446 -class_Fields_Ofield(A) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(A),B,C),D)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(A),B,C)) # label(fact_poly__mod__mult__right) # label(axiom).  [clausify(791)].
% 5.55/5.84  1447 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ominus__class_Ominus(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),B) # label(fact_diff__divide__eq__iff) # label(axiom).  [clausify(924)].
% 5.55/5.84  1448 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),B) # label(fact_divide__diff__eq__iff) # label(axiom).  [clausify(925)].
% 5.55/5.84  1449 -class_Fields_Ofield(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,E,C)) = c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_diff__frac__eq) # label(axiom).  [clausify(926)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),A) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)).  [resolve(1438,a,1439,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C).  [resolve(1438,a,1440,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B)).  [resolve(1438,a,1441,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B).  [resolve(1438,a,1442,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B).  [resolve(1438,a,1443,a)].
% 5.55/5.84  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)).  [resolve(1438,a,1445,a)].
% 5.55/5.84  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)).  [resolve(1438,a,1446,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C),A).  [resolve(1438,a,1447,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),A).  [resolve(1438,a,1448,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = B | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,D,B)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).  [resolve(1438,a,1449,a)].
% 5.55/5.84  1450 class_Fields_Ofield(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Fields_Ofield) # label(axiom).  [assumption].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)).  [resolve(1450,a,1439,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C).  [resolve(1450,a,1440,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)).  [resolve(1450,a,1441,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) != c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B).  [resolve(1450,a,1442,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,B) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B).  [resolve(1450,a,1443,a)].
% 5.55/5.84  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C)).  [resolve(1450,a,1445,a)].
% 5.55/5.84  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)).  [resolve(1450,a,1446,a)].
% 5.55/5.84  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C),A).  [resolve(1450,a,1447,a)].
% 5.76/5.97  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,B,A),C) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),A).  [resolve(1450,a,1448,a)].
% 5.76/5.97  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = B | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,C,A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,D,B)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)).  [resolve(1450,a,1449,a)].
% 5.76/5.97  1451 -class_Fields_Ofield(A) | class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom).  [clausify(1013)].
% 5.76/5.97  Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1451,a,1438,a)].
% 5.76/5.97  Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1451,a,1450,a)].
% 5.76/5.97  1452 -class_Fields_Ofield(A) | class_Divides_Oring__div(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Divides_Oring__div) # label(axiom).  [clausify(1025)].
% 5.76/5.97  Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1452,a,1438,a)].
% 5.76/5.97  Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1452,a,1450,a)].
% 5.76/5.97  1453 class_Fields_Olinordered__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field) # label(axiom).  [assumption].
% 5.76/5.97  1454 -class_Fields_Olinordered__field(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),c_Groups_Oabs__class_Oabs(A,B)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_nonzero__abs__divide) # label(axiom).  [clausify(162)].
% 5.76/5.97  1455 -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)) # label(fact_divide__strict__right__mono__neg) # label(axiom).  [clausify(218)].
% 5.76/5.97  1456 -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)) # label(fact_divide__strict__right__mono) # label(axiom).  [clausify(219)].
% 5.76/5.97  1457 -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)) # label(fact_divide__neg__neg) # label(axiom).  [clausify(220)].
% 5.76/5.97  1458 -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)) # label(fact_divide__neg__pos) # label(axiom).  [clausify(221)].
% 5.76/5.97  1459 -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)) # label(fact_divide__pos__neg) # label(axiom).  [clausify(222)].
% 5.76/5.97  1460 -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)) # label(fact_divide__pos__pos) # label(axiom).  [clausify(223)].
% 5.76/5.97  1461 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__nonneg__pos) # label(axiom).  [clausify(226)].
% 5.76/5.97  1462 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonneg__neg) # label(axiom).  [clausify(227)].
% 5.76/5.97  1463 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_frac__less2) # label(axiom).  [clausify(228)].
% 5.76/5.97  1464 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(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)) # label(fact_frac__less) # label(axiom).  [clausify(229)].
% 5.76/5.97  1465 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,E),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_frac__le) # label(axiom).  [clausify(230)].
% 5.76/5.97  1466 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__nonpos__pos) # label(axiom).  [clausify(231)].
% 5.76/5.97  1467 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_divide__nonpos__neg) # label(axiom).  [clausify(232)].
% 5.76/5.97  1468 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__less__divide__eq) # label(axiom).  [clausify(235)].
% 5.76/5.97  1469 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__less__divide__eq) # label(axiom).  [clausify(235)].
% 5.76/5.97  1470 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__less__eq) # label(axiom).  [clausify(236)].
% 5.76/5.97  1471 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__less__eq) # label(axiom).  [clausify(236)].
% 5.76/5.97  1472 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) | c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_mult__imp__div__pos__less) # label(axiom).  [clausify(237)].
% 5.76/5.97  1473 -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(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)) # label(fact_mult__imp__less__div__pos) # label(axiom).  [clausify(238)].
% 5.76/5.97  1474 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__less__divide__eq) # label(axiom).  [clausify(239)].
% 5.76/5.97  1475 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__less__divide__eq) # label(axiom).  [clausify(239)].
% 5.76/5.97  1476 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__less__eq) # label(axiom).  [clausify(240)].
% 5.76/5.97  1477 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__less__eq) # label(axiom).  [clausify(240)].
% 5.76/5.97  1478 -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(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)) # label(fact_divide__strict__left__mono) # label(axiom).  [clausify(241)].
% 5.76/5.97  1479 -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(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)) # label(fact_divide__strict__left__mono__neg) # label(axiom).  [clausify(242)].
% 5.76/5.97  1480 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,C),c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_divide__left__mono) # label(axiom).  [clausify(277)].
% 5.76/5.97  1481 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__le__eq) # label(axiom).  [clausify(278)].
% 5.76/5.97  1482 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),C) # label(fact_neg__divide__le__eq) # label(axiom).  [clausify(278)].
% 5.76/5.97  1483 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__le__divide__eq) # label(axiom).  [clausify(279)].
% 5.76/5.97  1484 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) # label(fact_neg__le__divide__eq) # label(axiom).  [clausify(279)].
% 5.76/5.97  1485 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) # label(fact_mult__imp__le__div__pos) # label(axiom).  [clausify(280)].
% 5.76/5.97  1486 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) # label(fact_mult__imp__div__pos__le) # label(axiom).  [clausify(281)].
% 5.76/5.97  1487 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__le__eq) # label(axiom).  [clausify(282)].
% 5.76/5.97  1488 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,B),D) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) # label(fact_pos__divide__le__eq) # label(axiom).  [clausify(282)].
% 5.76/5.97  1489 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__le__divide__eq) # label(axiom).  [clausify(283)].
% 5.76/5.97  1490 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Rings_Oinverse__class_Odivide(A,D,B)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),D) # label(fact_pos__le__divide__eq) # label(axiom).  [clausify(283)].
% 5.76/5.97  1491 -class_Fields_Olinordered__field(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),f19(B,C,A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__epsilon) # label(axiom).  [clausify(455)].
% 5.76/5.97  1492 -class_Fields_Olinordered__field(A) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Oplus__class_Oplus(A,C,f19(C,B,A))) | c_Orderings_Oord__class_Oless__eq(A,B,C) # label(fact_field__le__epsilon) # label(axiom).  [clausify(455)].
% 5.76/5.97  1493 -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) # label(fact_gt__half__sum) # label(axiom).  [clausify(491)].
% 5.76/5.97  1494 -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)))) # label(fact_less__half__sum) # label(axiom).  [clausify(492)].
% 5.76/5.98  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)).  [resolve(1453,a,1454,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)).  [resolve(1453,a,1455,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1453,a,1456,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1453,a,1457,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1453,a,1458,a)].
% 5.76/5.98  Derived: -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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1453,a,1459,a)].
% 5.76/5.98  Derived: -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),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1453,a,1460,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1453,a,1461,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1453,a,1462,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -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,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1453,a,1463,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1453,a,1464,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,D),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1453,a,1465,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1453,a,1466,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1453,a,1467,a)].
% 5.76/5.98  Derived: -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,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),C).  [resolve(1453,a,1468,a)].
% 5.76/5.98  Derived: -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,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),C).  [resolve(1453,a,1469,a)].
% 5.76/5.98  Derived: -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,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)).  [resolve(1453,a,1470,a)].
% 5.76/5.98  Derived: -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,B,A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)).  [resolve(1453,a,1471,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)).  [resolve(1453,a,1474,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)).  [resolve(1453,a,1475,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B).  [resolve(1453,a,1476,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B).  [resolve(1453,a,1477,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)).  [resolve(1453,a,1478,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)).  [resolve(1453,a,1479,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)).  [resolve(1453,a,1480,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B).  [resolve(1453,a,1481,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B).  [resolve(1453,a,1482,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)).  [resolve(1453,a,1483,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)).  [resolve(1453,a,1484,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)).  [resolve(1453,a,1485,a)].
% 5.76/5.98  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C).  [resolve(1453,a,1486,a)].
% 5.87/6.11  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)).  [resolve(1453,a,1487,a)].
% 5.87/6.11  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),C).  [resolve(1453,a,1489,a)].
% 5.87/6.11  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f19(A,B,tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A).  [resolve(1453,a,1491,a)].
% 5.87/6.11  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,f19(B,A,tc_RealDef_Oreal))) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B).  [resolve(1453,a,1492,a)].
% 5.87/6.11  Derived: -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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),B).  [resolve(1453,a,1493,a)].
% 5.87/6.11  Derived: -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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).  [resolve(1453,a,1494,a)].
% 5.87/6.11  1495 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 5.87/6.11  1496 -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)) # label(fact_add__strict__mono) # label(axiom).  [clausify(211)].
% 5.87/6.11  1497 -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)) # label(fact_add__strict__left__mono) # label(axiom).  [clausify(212)].
% 5.87/6.11  1498 -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)) # label(fact_add__strict__right__mono) # label(axiom).  [clausify(213)].
% 5.87/6.11  1499 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_add__le__less__mono) # label(axiom).  [clausify(265)].
% 5.87/6.11  1500 -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(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)) # label(fact_add__less__le__mono) # label(axiom).  [clausify(266)].
% 5.87/6.11  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(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)).  [resolve(1495,a,1496,a)].
% 5.87/6.11  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(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)).  [resolve(1495,a,1499,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(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)).  [resolve(1495,a,1500,a)].
% 6.05/6.24  1501 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 6.05/6.24  Derived: -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)).  [resolve(1501,a,1496,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless__eq(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)).  [resolve(1501,a,1499,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(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)).  [resolve(1501,a,1500,a)].
% 6.05/6.24  1502 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1502,a,1496,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1502,a,1499,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,D)).  [resolve(1502,a,1500,a)].
% 6.05/6.24  1503 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) # label(axiom).  [clausify(982)].
% 6.05/6.24  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)).  [resolve(1503,b,1496,a)].
% 6.05/6.24  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)).  [resolve(1503,b,1499,a)].
% 6.05/6.24  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,E)).  [resolve(1503,b,1500,a)].
% 6.05/6.24  1504 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) # label(axiom).  [assumption].
% 6.05/6.24  1505 -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)) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1506 -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) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1507 -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)) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1508 -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) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1509 -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)) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1510 -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) # label(fact_divide__less__0__iff) # label(axiom).  [clausify(224)].
% 6.05/6.24  1511 -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)) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1512 -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)) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1513 -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)) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1514 -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)) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1515 -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) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1516 -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)) # label(fact_zero__less__divide__iff) # label(axiom).  [clausify(225)].
% 6.05/6.24  1517 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1518 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1519 -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)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1520 -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)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1521 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1522 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1523 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1524 -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(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)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1525 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1526 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_less__divide__eq) # label(axiom).  [clausify(233)].
% 6.05/6.24  1527 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1528 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1529 -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) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1530 -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) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1531 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1532 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1533 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1534 -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(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) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1535 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1536 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__less__eq) # label(axiom).  [clausify(234)].
% 6.05/6.24  1537 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,C),B) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,C,B)) # label(fact_abs__div__pos) # label(axiom).  [clausify(267)].
% 6.05/6.24  1538 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,D,B),c_Rings_Oinverse__class_Odivide(A,D,C)) # label(fact_divide__left__mono__neg) # label(axiom).  [clausify(276)].
% 6.05/6.24  1539 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1540 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1541 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1542 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1543 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1544 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1545 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1546 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1547 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1548 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),D) | -c_Orderings_Oord__class_Oless__eq(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_divide__le__eq) # label(axiom).  [clausify(284)].
% 6.05/6.24  1549 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1550 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1551 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1552 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1553 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1554 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(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__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1555 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1556 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(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__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1557 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1558 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,B,c_Rings_Oinverse__class_Odivide(A,C,D)) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) | -c_Orderings_Oord__class_Oless__eq(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_le__divide__eq) # label(axiom).  [clausify(285)].
% 6.05/6.24  1559 -class_Fields_Olinordered__field__inverse__zero(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)) = c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Odivide(A,B,C)) # label(fact_abs__divide) # label(axiom).  [clausify(312)].
% 6.05/6.24  1560 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1561 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1562 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1563 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1564 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1565 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Odivide(A,B,C)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_zero__le__divide__iff) # label(axiom).  [clausify(313)].
% 6.05/6.24  1566 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1567 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1568 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1569 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1570 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A)) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1571 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,C),c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) # label(fact_divide__le__0__iff) # label(axiom).  [clausify(314)].
% 6.05/6.24  1572 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,B,D),c_Rings_Oinverse__class_Odivide(A,C,D)) # label(fact_divide__right__mono) # label(axiom).  [clausify(315)].
% 6.05/6.24  1573 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Ozero__class_Ozero(A)) | c_Orderings_Oord__class_Oless__eq(A,c_Rings_Oinverse__class_Odivide(A,C,D),c_Rings_Oinverse__class_Odivide(A,B,D)) # label(fact_divide__right__mono__neg) # label(axiom).  [clausify(316)].
% 6.05/6.24  1574 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),f20(B,C,A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom).  [clausify(496)].
% 6.05/6.24  1575 -class_Fields_Olinordered__field__inverse__zero(A) | c_Orderings_Oord__class_Oless(A,f20(B,C,A),c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom).  [clausify(496)].
% 6.05/6.24  1576 -class_Fields_Olinordered__field__inverse__zero(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),f20(B,C,A)),C),B) | c_Orderings_Oord__class_Oless__eq(A,C,B) # label(fact_field__le__mult__one__interval) # label(axiom).  [clausify(496)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1505,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1504,a,1506,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,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)).  [resolve(1504,a,1507,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,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).  [resolve(1504,a,1508,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1511,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1512,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1513,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1514,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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,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)).  [resolve(1504,a,1519,a)].
% 6.05/6.24  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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,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)).  [resolve(1504,a,1520,a)].
% 6.05/6.24  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1522,a)].
% 6.05/6.24  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | 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,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1524,a)].
% 6.05/6.24  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | 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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1529,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | 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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1530,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | 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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1532,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1534,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),A) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,A)).  [resolve(1504,a,1537,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,C,B)).  [resolve(1504,a,1538,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | 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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1541,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | 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,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1542,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1544,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1546,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C).  [resolve(1504,a,1548,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1551,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1552,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1554,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1556,a)].
% 6.05/6.25  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1558,a)].
% 6.05/6.25  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B)).  [resolve(1504,a,1559,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1561,a)].
% 6.05/6.25  Derived: -c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1562,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1504,a,1564,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless__eq(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__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1565,a)].
% 6.18/6.37  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1504,a,1567,a)].
% 6.18/6.37  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1568,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1504,a,1570,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B).  [resolve(1504,a,1571,a)].
% 6.18/6.37  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C)).  [resolve(1504,a,1572,a)].
% 6.18/6.37  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,B,C),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,A,C)).  [resolve(1504,a,1573,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),f20(A,B,tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A).  [resolve(1504,a,1574,a)].
% 6.18/6.37  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,f20(A,B,tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A).  [resolve(1504,a,1575,a)].
% 6.18/6.37  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),f20(A,B,tc_RealDef_Oreal)),B),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B,A).  [resolve(1504,a,1576,a)].
% 6.18/6.37  1577 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
% 6.18/6.37  1578 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_mult__pos__pos) # label(axiom).  [clausify(247)].
% 6.18/6.37  1579 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg) # label(axiom).  [clausify(248)].
% 6.18/6.37  1580 -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(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__pos__neg2) # label(axiom).  [clausify(249)].
% 6.18/6.37  1581 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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) # label(fact_zero__less__mult__pos) # label(axiom).  [clausify(250)].
% 6.18/6.37  1582 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(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) # label(fact_zero__less__mult__pos2) # label(axiom).  [clausify(251)].
% 6.18/6.37  1583 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__neg__pos) # label(axiom).  [clausify(253)].
% 6.18/6.37  1584 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_mult__strict__right__mono) # label(axiom).  [clausify(255)].
% 6.18/6.37  1585 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_mult__strict__left__mono) # label(axiom).  [clausify(256)].
% 6.18/6.37  1586 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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__eq(A,C,D) # label(fact_mult__left__le__imp__le) # label(axiom).  [clausify(286)].
% 6.18/6.37  1587 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(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__eq(A,B,D) # label(fact_mult__right__le__imp__le) # label(axiom).  [clausify(287)].
% 6.18/6.37  1588 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__less__imp__less__left) # label(axiom).  [clausify(288)].
% 6.18/6.37  1589 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__less__imp__less__right) # label(axiom).  [clausify(290)].
% 6.18/6.38  1590 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless__eq(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__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__le__less__imp__less) # label(axiom).  [clausify(292)].
% 6.18/6.38  1591 -class_Rings_Olinordered__semiring__strict(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) | -c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__less__le__imp__less) # label(axiom).  [clausify(293)].
% 6.18/6.38  1592 -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__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__strict__mono_H) # label(axiom).  [clausify(294)].
% 6.18/6.38  1593 -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__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_mult__strict__mono) # label(axiom).  [clausify(295)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).  [resolve(1577,a,1578,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1577,a,1579,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1577,a,1580,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).  [resolve(1577,a,1581,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).  [resolve(1577,a,1582,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,C).  [resolve(1577,a,1587,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).  [resolve(1577,a,1588,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C).  [resolve(1577,a,1589,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1577,a,1590,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(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) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1577,a,1591,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1577,a,1592,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)).  [resolve(1577,a,1593,a)].
% 6.18/6.38  1594 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)).  [resolve(1594,a,1578,a)].
% 6.18/6.38  Derived: -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_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1594,a,1579,a)].
% 6.18/6.38  Derived: -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_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1594,a,1580,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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).  [resolve(1594,a,1581,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(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) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).  [resolve(1594,a,1582,a)].
% 6.18/6.38  Derived: -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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1594,a,1584,a)].
% 6.18/6.38  Derived: -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(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)).  [resolve(1594,a,1585,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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__eq(tc_Nat_Onat,B,C).  [resolve(1594,a,1586,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(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__eq(tc_Nat_Onat,A,C).  [resolve(1594,a,1587,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).  [resolve(1594,a,1588,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).  [resolve(1594,a,1589,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(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_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1594,a,1590,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1594,a,1591,a)].
% 6.18/6.38  Derived: -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__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1594,a,1592,a)].
% 6.18/6.38  Derived: -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_Ozero__class_Ozero(tc_Nat_Onat),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).  [resolve(1594,a,1593,a)].
% 6.18/6.38  1595 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) # label(axiom).  [assumption].
% 6.18/6.38  Derived: -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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).  [resolve(1595,a,1578,a)].
% 6.18/6.38  Derived: -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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1595,a,1579,a)].
% 6.18/6.38  Derived: -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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1595,a,1580,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | -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).  [resolve(1595,a,1581,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) | -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),A).  [resolve(1595,a,1582,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,C).  [resolve(1595,a,1587,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).  [resolve(1595,a,1588,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C).  [resolve(1595,a,1589,a)].
% 6.18/6.38  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1595,a,1590,a)].
% 6.18/6.39  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(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) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1595,a,1591,a)].
% 6.18/6.39  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1595,a,1592,a)].
% 6.18/6.39  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)).  [resolve(1595,a,1593,a)].
% 6.18/6.39  1596 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) # label(axiom).  [clausify(986)].
% 6.18/6.39  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1596,b,1578,a)].
% 6.18/6.39  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1596,b,1579,a)].
% 6.18/6.39  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1596,b,1580,a)].
% 6.18/6.39  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C).  [resolve(1596,b,1581,a)].
% 6.18/6.39  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B).  [resolve(1596,b,1582,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,D).  [resolve(1596,b,1587,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D).  [resolve(1596,b,1588,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D).  [resolve(1596,b,1589,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1596,b,1590,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1596,b,1591,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1596,b,1592,a)].
% 6.31/6.51  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)).  [resolve(1596,b,1593,a)].
% 6.31/6.51  1597 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
% 6.43/6.64  1598 -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(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) # label(fact_comm__mult__strict__left__mono) # label(axiom).  [clausify(257)].
% 6.43/6.64  1599 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
% 6.43/6.64  1600 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) # label(axiom).  [assumption].
% 6.43/6.64  1601 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) # label(axiom).  [clausify(984)].
% 6.43/6.64  1602 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom).  [assumption].
% 6.43/6.64  1603 -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)) # label(fact_pos__add__strict) # label(axiom).  [clausify(263)].
% 6.43/6.64  1604 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__le__zero) # label(axiom).  [clausify(475)].
% 6.43/6.64  1605 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__le__one) # label(axiom).  [clausify(476)].
% 6.43/6.64  1606 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_not__one__less__zero) # label(axiom).  [clausify(477)].
% 6.43/6.64  1607 -class_Rings_Olinordered__semidom(A) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)) # label(fact_zero__less__one) # label(axiom).  [clausify(478)].
% 6.43/6.64  1608 -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(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) # label(fact_less__1__mult) # label(axiom).  [clausify(479)].
% 6.43/6.64  1609 -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))) # label(fact_less__add__one) # label(axiom).  [clausify(480)].
% 6.43/6.64  1610 -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))) # label(fact_zero__less__two) # label(axiom).  [clausify(490)].
% 6.43/6.64  1611 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless__eq(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,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__strict__mono) # label(axiom).  [clausify(554)].
% 6.43/6.64  1612 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_one__less__power) # label(axiom).  [clausify(555)].
% 6.43/6.64  1613 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__increasing__iff) # label(axiom).  [clausify(556)].
% 6.43/6.64  1614 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__increasing__iff) # label(axiom).  [clausify(556)].
% 6.43/6.64  1615 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) # label(fact_power__le__imp__le__exp) # label(axiom).  [clausify(557)].
% 6.43/6.64  1616 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_zero__le__power) # label(axiom).  [clausify(571)].
% 6.43/6.64  1617 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mono) # label(axiom).  [clausify(572)].
% 6.43/6.64  1618 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_zero__less__power) # label(axiom).  [clausify(573)].
% 6.43/6.64  1619 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_one__le__power) # label(axiom).  [clausify(574)].
% 6.43/6.64  1620 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C = D # label(fact_power__inject__exp) # label(axiom).  [clausify(576)].
% 6.43/6.64  1621 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C != D # label(fact_power__inject__exp) # label(axiom).  [clausify(576)].
% 6.43/6.64  1622 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_power__less__imp__less__base) # label(axiom).  [clausify(581)].
% 6.43/6.64  1623 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__less__power__Suc) # label(axiom).  [clausify(582)].
% 6.43/6.64  1624 -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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__gt1__lemma) # label(axiom).  [clausify(583)].
% 6.43/6.64  1625 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) # label(fact_power__strict__increasing) # label(axiom).  [clausify(586)].
% 6.43/6.64  1626 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__less__imp__less__exp) # label(axiom).  [clausify(587)].
% 6.43/6.64  1627 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__strict__increasing__iff) # label(axiom).  [clausify(588)].
% 6.43/6.64  1628 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D) # label(fact_power__strict__increasing__iff) # label(axiom).  [clausify(588)].
% 6.43/6.64  1629 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oone__class_Oone(A),D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)) # label(fact_power__increasing) # label(axiom).  [clausify(589)].
% 6.43/6.64  1630 -class_Rings_Olinordered__semidom(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__Suc__less) # label(axiom).  [clausify(590)].
% 6.43/6.64  1631 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)) # label(fact_power__strict__decreasing) # label(axiom).  [clausify(591)].
% 6.43/6.64  1632 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | B = D # label(fact_power__eq__imp__eq__base) # label(axiom).  [clausify(592)].
% 6.43/6.64  1633 -class_Rings_Olinordered__semidom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),D) | -c_Orderings_Oord__class_Oless__eq(A,D,c_Groups_Oone__class_Oone(A)) | c_Orderings_Oord__class_Oless__eq(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)) # label(fact_power__decreasing) # label(axiom).  [clausify(593)].
% 6.43/6.64  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C)).  [resolve(1602,a,1603,a)].
% 6.43/6.64  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1602,a,1604,a)].
% 6.43/6.64  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).  [resolve(1602,a,1605,a)].
% 6.43/6.64  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1602,a,1606,a)].
% 6.43/6.64  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).  [resolve(1602,a,1607,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).  [resolve(1602,a,1608,a)].
% 6.43/6.65  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))).  [resolve(1602,a,1609,a)].
% 6.43/6.65  Derived: 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),c_Groups_Oone__class_Oone(tc_Int_Oint))).  [resolve(1602,a,1610,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)).  [resolve(1602,a,1611,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1602,a,1612,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1602,a,1613,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1602,a,1614,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1602,a,1616,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)).  [resolve(1602,a,1617,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1602,a,1618,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1602,a,1619,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B = C.  [resolve(1602,a,1620,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B != C.  [resolve(1602,a,1621,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C).  [resolve(1602,a,1622,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))).  [resolve(1602,a,1623,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))).  [resolve(1602,a,1624,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)).  [resolve(1602,a,1625,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).  [resolve(1602,a,1626,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),C) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)).  [resolve(1602,a,1629,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1602,a,1630,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,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,C,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)).  [resolve(1602,a,1631,a)].
% 6.43/6.65  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C.  [resolve(1602,a,1632,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,c_Groups_Oone__class_Oone(tc_Int_Oint)) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)).  [resolve(1602,a,1633,a)].
% 6.43/6.65  1634 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom).  [assumption].
% 6.43/6.65  Derived: -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) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).  [resolve(1634,a,1603,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1634,a,1604,a)].
% 6.43/6.65  Derived: c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)).  [resolve(1634,a,1605,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).  [resolve(1634,a,1606,a)].
% 6.43/6.65  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)).  [resolve(1634,a,1607,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)).  [resolve(1634,a,1608,a)].
% 6.43/6.65  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))).  [resolve(1634,a,1609,a)].
% 6.43/6.65  Derived: c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))).  [resolve(1634,a,1610,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)).  [resolve(1634,a,1611,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1634,a,1612,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1634,a,1613,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1634,a,1614,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1634,a,1616,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)).  [resolve(1634,a,1617,a)].
% 6.43/6.65  Derived: -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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1634,a,1618,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1634,a,1619,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B = C.  [resolve(1634,a,1620,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B != C.  [resolve(1634,a,1621,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).  [resolve(1634,a,1622,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))).  [resolve(1634,a,1623,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))).  [resolve(1634,a,1624,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)).  [resolve(1634,a,1625,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).  [resolve(1634,a,1626,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)).  [resolve(1634,a,1629,a)].
% 6.43/6.65  Derived: -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,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1634,a,1630,a)].
% 6.43/6.65  Derived: -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,C,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)).  [resolve(1634,a,1631,a)].
% 6.43/6.65  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C.  [resolve(1634,a,1632,a)].
% 6.43/6.65  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,c_Groups_Oone__class_Oone(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)).  [resolve(1634,a,1633,a)].
% 6.43/6.66  1635 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semidom) # label(axiom).  [assumption].
% 6.43/6.66  Derived: -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,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,C)).  [resolve(1635,a,1603,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1635,a,1604,a)].
% 6.43/6.66  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).  [resolve(1635,a,1605,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1635,a,1606,a)].
% 6.43/6.66  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).  [resolve(1635,a,1607,a)].
% 6.43/6.66  Derived: -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_Oone__class_Oone(tc_RealDef_Oreal),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1608,a)].
% 6.43/6.66  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).  [resolve(1635,a,1609,a)].
% 6.43/6.66  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).  [resolve(1635,a,1610,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)).  [resolve(1635,a,1611,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1612,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1635,a,1613,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).  [resolve(1635,a,1614,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1616,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)).  [resolve(1635,a,1617,a)].
% 6.43/6.66  Derived: -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(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1618,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1619,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B = C.  [resolve(1635,a,1620,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | B != C.  [resolve(1635,a,1621,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,C).  [resolve(1635,a,1622,a)].
% 6.43/6.66  Derived: -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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))).  [resolve(1635,a,1623,a)].
% 6.43/6.66  Derived: -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_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))).  [resolve(1635,a,1624,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)).  [resolve(1635,a,1625,a)].
% 6.43/6.66  Derived: -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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).  [resolve(1635,a,1626,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),C) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B)).  [resolve(1635,a,1629,a)].
% 6.43/6.66  Derived: -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(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1635,a,1630,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B) | -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,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)).  [resolve(1635,a,1631,a)].
% 6.43/6.66  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) | A = C.  [resolve(1635,a,1632,a)].
% 6.43/6.66  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)).  [resolve(1635,a,1633,a)].
% 6.43/6.66  1636 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semidom) # label(axiom).  [clausify(1001)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)).  [resolve(1636,b,1603,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1636,b,1604,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))).  [resolve(1636,b,1605,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1636,b,1606,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))).  [resolve(1636,b,1607,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1608,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))).  [resolve(1636,b,1609,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))).  [resolve(1636,b,1610,a)].
% 6.43/6.66  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1636,b,1611,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(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_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1612,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D).  [resolve(1636,b,1613,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D).  [resolve(1636,b,1614,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1616,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1636,b,1617,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1618,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1619,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C = D.  [resolve(1636,b,1620,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | C != D.  [resolve(1636,b,1621,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,D).  [resolve(1636,b,1622,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))).  [resolve(1636,b,1623,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C))).  [resolve(1636,b,1624,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)).  [resolve(1636,b,1625,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).  [resolve(1636,b,1626,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),D) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C)).  [resolve(1636,b,1629,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1636,b,1630,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)).  [resolve(1636,b,1631,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) | B = D.  [resolve(1636,b,1632,a)].
% 6.43/6.67  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),B)).  [resolve(1636,b,1633,a)].
% 6.73/6.94  1637 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom).  [assumption].
% 6.73/6.94  1638 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B) | c_Orderings_Oord__class_Oless(A,C,D) # label(fact_mult__left__less__imp__less) # label(axiom).  [clausify(289)].
% 6.73/6.94  1639 -class_Rings_Olinordered__semiring(A) | -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C) | c_Orderings_Oord__class_Oless(A,B,D) # label(fact_mult__right__less__imp__less) # label(axiom).  [clausify(291)].
% 6.73/6.94  1640 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom).  [assumption].
% 6.73/6.94  1641 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring) # label(axiom).  [assumption].
% 6.73/6.94  1642 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring) # label(axiom).  [clausify(1000)].
% 6.73/6.94  1643 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom).  [assumption].
% 6.73/6.94  1644 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,B) != c_Polynomial_Opoly(A,C) | B = C # label(fact_poly__eq__iff) # label(axiom).  [clausify(329)].
% 6.73/6.94  1645 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,B) = c_Polynomial_Opoly(A,C) | B != C # label(fact_poly__eq__iff) # label(axiom).  [clausify(329)].
% 6.73/6.94  1646 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) != c_Polynomial_Opoly(A,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B # label(fact_poly__zero) # label(axiom).  [clausify(330)].
% 6.73/6.94  1647 -class_Int_Oring__char__0(A) | -class_Rings_Oidom(A) | c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_Polynomial_Opoly(A,B) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != B # label(fact_poly__zero) # label(axiom).  [clausify(330)].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) != c_Polynomial_Opoly(tc_Int_Oint,B) | A = B.  [resolve(1643,a,1644,a)].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_Int_Oint) | c_Polynomial_Opoly(tc_Int_Oint,A) = c_Polynomial_Opoly(tc_Int_Oint,B) | A != B.  [resolve(1643,a,1645,a)].
% 6.73/6.94  1648 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Int_Oring__char__0) # label(axiom).  [assumption].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(tc_RealDef_Oreal,A) != c_Polynomial_Opoly(tc_RealDef_Oreal,B) | A = B.  [resolve(1648,a,1644,a)].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(tc_RealDef_Oreal,A) = c_Polynomial_Opoly(tc_RealDef_Oreal,B) | A != B.  [resolve(1648,a,1645,a)].
% 6.73/6.94  1649 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom).  [assumption].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) != c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A = B.  [resolve(1649,a,1644,a)].
% 6.73/6.94  Derived: -class_Rings_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(tc_Complex_Ocomplex,A) = c_Polynomial_Opoly(tc_Complex_Ocomplex,B) | A != B.  [resolve(1649,a,1645,a)].
% 6.73/6.94  1650 -class_Rings_Olinordered__idom(A) | class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom).  [clausify(1029)].
% 6.73/6.94  Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) != c_Polynomial_Opoly(tc_Polynomial_Opoly(A),C) | B = C.  [resolve(1650,b,1644,a)].
% 6.97/7.21  Derived: -class_Rings_Olinordered__idom(A) | -class_Rings_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(tc_Polynomial_Opoly(A),B) = c_Polynomial_Opoly(tc_Polynomial_Opoly(A),C) | B != C.  [resolve(1650,b,1645,a)].
% 6.97/7.21  1651 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom).  [assumption].
% 6.97/7.21  1652 -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__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oone__class_Oone(A) != c_Groups_Oplus__class_Oplus(A,E,F) | c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C) # label(fact_convex__bound__lt) # label(axiom).  [clausify(454)].
% 6.97/7.21  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),E) | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,E) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C)),B).  [resolve(1651,a,1652,a)].
% 6.97/7.21  1653 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) # label(axiom).  [assumption].
% 6.97/7.21  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),E) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,E) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C)),B).  [resolve(1653,a,1652,a)].
% 6.97/7.21  1654 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) # label(axiom).  [clausify(985)].
% 6.97/7.21  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),E,F) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D)),C).  [resolve(1654,b,1652,a)].
% 6.97/7.21  1655 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom).  [assumption].
% 6.97/7.21  1656 -class_RealVector_Oreal__normed__algebra__1(A) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A)) # label(fact_norm__one) # label(axiom).  [clausify(457)].
% 6.97/7.21  1657 -class_RealVector_Oreal__normed__algebra__1(A) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C)) # label(fact_norm__power__ineq) # label(axiom).  [clausify(535)].
% 7.16/7.34  Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).  [resolve(1655,a,1656,a)].
% 7.16/7.34  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,A)),B)).  [resolve(1655,a,1657,a)].
% 7.16/7.34  1658 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom).  [assumption].
% 7.16/7.34  Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).  [resolve(1658,a,1656,a)].
% 7.16/7.34  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A)),B)).  [resolve(1658,a,1657,a)].
% 7.16/7.34  1659 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom).  [assumption].
% 7.16/7.34  1660 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1__left) # label(axiom).  [clausify(463)].
% 7.16/7.34  1661 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom).  [clausify(465)].
% 7.16/7.34  1662 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__commutes) # label(axiom).  [clausify(565)].
% 7.16/7.34  1663 -class_Groups_Omonoid__mult(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_power__one) # label(axiom).  [clausify(566)].
% 7.16/7.34  1664 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) # label(fact_power__mult) # label(axiom).  [clausify(569)].
% 7.16/7.34  1665 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_power__one__right) # label(axiom).  [clausify(570)].
% 7.16/7.34  1666 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(fact_power__add) # label(axiom).  [clausify(579)].
% 7.16/7.34  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A.  [resolve(1659,a,1660,a)].
% 7.16/7.34  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A.  [resolve(1659,a,1661,a)].
% 7.16/7.34  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).  [resolve(1659,a,1662,a)].
% 7.16/7.34  Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A).  [resolve(1659,a,1663,a)].
% 7.16/7.34  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1659,a,1664,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1659,a,1665,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)).  [resolve(1659,a,1666,a)].
% 7.16/7.35  1667 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom).  [assumption].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A.  [resolve(1667,a,1660,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1667,a,1661,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)).  [resolve(1667,a,1662,a)].
% 7.16/7.35  Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A).  [resolve(1667,a,1663,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1667,a,1664,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1667,a,1665,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)).  [resolve(1667,a,1666,a)].
% 7.16/7.35  1668 class_Groups_Omonoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Omonoid__mult) # label(axiom).  [assumption].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A) = A.  [resolve(1668,a,1660,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = A.  [resolve(1668,a,1661,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)).  [resolve(1668,a,1662,a)].
% 7.16/7.35  Derived: c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A).  [resolve(1668,a,1663,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1668,a,1664,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1668,a,1665,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)).  [resolve(1668,a,1666,a)].
% 7.16/7.35  1669 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Omonoid__mult) # label(axiom).  [assumption].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A.  [resolve(1669,a,1660,a)].
% 7.16/7.35  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = A.  [resolve(1669,a,1661,a)].
% 7.28/7.49  Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)).  [resolve(1669,a,1662,a)].
% 7.28/7.49  Derived: c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),A).  [resolve(1669,a,1663,a)].
% 7.28/7.49  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).  [resolve(1669,a,1664,a)].
% 7.28/7.49  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1669,a,1665,a)].
% 7.28/7.49  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)).  [resolve(1669,a,1666,a)].
% 7.28/7.49  1670 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Omonoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Omonoid__mult) # label(axiom).  [clausify(1020)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B) = B.  [resolve(1670,b,1660,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B.  [resolve(1670,b,1661,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)).  [resolve(1670,b,1662,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B).  [resolve(1670,b,1663,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).  [resolve(1670,b,1664,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B.  [resolve(1670,b,1665,a)].
% 7.28/7.49  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)).  [resolve(1670,b,1666,a)].
% 7.28/7.49  1671 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 7.28/7.49  1672 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1) # label(axiom).  [clausify(464)].
% 7.28/7.49  1673 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult_Ocomm__neutral) # label(axiom).  [clausify(466)].
% 7.28/7.49  1674 -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_power__mult__distrib) # label(axiom).  [clausify(564)].
% 7.40/7.63  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)).  [resolve(1671,a,1674,a)].
% 7.40/7.63  1675 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 7.40/7.63  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)).  [resolve(1675,a,1674,a)].
% 7.40/7.63  1676 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 7.40/7.63  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)).  [resolve(1676,a,1674,a)].
% 7.40/7.63  1677 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 7.40/7.63  Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)).  [resolve(1677,a,1674,a)].
% 7.40/7.63  1678 -class_Rings_Ocomm__semiring__1(A) | class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) # label(axiom).  [clausify(1003)].
% 7.40/7.63  Derived: -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)).  [resolve(1678,b,1674,a)].
% 7.40/7.63  1679 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom).  [assumption].
% 7.40/7.63  1680 -class_Rings_Olinordered__semiring__1(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),E) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),F) | c_Groups_Oone__class_Oone(A) != c_Groups_Oplus__class_Oplus(A,E,F) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C) # label(fact_convex__bound__le) # label(axiom).  [clausify(494)].
% 7.40/7.63  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),E) | c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,D,E) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C)),B).  [resolve(1679,a,1680,a)].
% 7.40/7.63  1681 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Olinordered__semiring__1) # label(axiom).  [assumption].
% 7.69/7.90  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),E) | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,D,E) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),E),C)),B).  [resolve(1681,a,1680,a)].
% 7.69/7.90  1682 -class_Rings_Olinordered__idom(A) | class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) # label(axiom).  [clausify(997)].
% 7.69/7.90  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),F) | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),E,F) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),F),D)),C).  [resolve(1682,b,1680,a)].
% 7.69/7.90  1683 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
% 7.69/7.90  1684 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) # label(fact_field__power__not__zero) # label(axiom).  [clausify(563)].
% 7.69/7.90  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B).  [resolve(1683,a,1684,a)].
% 7.69/7.90  1685 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
% 7.69/7.90  Derived: c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B).  [resolve(1685,a,1684,a)].
% 7.69/7.90  1686 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
% 7.69/7.90  Derived: c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B).  [resolve(1686,a,1684,a)].
% 7.69/7.90  1687 -class_Rings_Oidom(A) | class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) # label(axiom).  [clausify(992)].
% 7.69/7.90  Derived: -class_Rings_Oidom(A) | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C).  [resolve(1687,b,1684,a)].
% 7.69/7.90  1688 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom).  [assumption].
% 7.69/7.90  1689 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom).  [clausify(584)].
% 7.69/7.90  1690 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom).  [clausify(584)].
% 7.69/7.90  1691 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,f53(C,B,A),c_Groups_Ozero__class_Ozero(A))) # label(fact_unity__coeff__ex) # label(axiom).  [clausify(889)].
% 7.69/7.90  1692 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(B,f53(C,B,A))) # label(fact_unity__coeff__ex) # label(axiom).  [clausify(889)].
% 7.69/7.90  1693 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f54(C,B,A)))) | -c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,D,c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(B,D)) # label(fact_unity__coeff__ex) # label(axiom).  [clausify(889)].
% 7.69/7.90  Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A).  [resolve(1688,a,1689,b)].
% 7.69/7.90  Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A).  [resolve(1688,a,1690,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,f53(B,A,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(1688,a,1691,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | hBOOL(hAPP(A,f53(B,A,tc_Int_Oint))).  [resolve(1688,a,1692,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Int_Oint) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),f54(B,A,tc_Int_Oint)))) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(A,C)).  [resolve(1688,a,1693,b)].
% 7.69/7.90  1694 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom).  [assumption].
% 7.69/7.90  Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A).  [resolve(1694,a,1689,b)].
% 7.69/7.90  Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A).  [resolve(1694,a,1690,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,f53(B,A,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).  [resolve(1694,a,1691,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | hBOOL(hAPP(A,f53(B,A,tc_Nat_Onat))).  [resolve(1694,a,1692,b)].
% 7.69/7.90  Derived: -class_Rings_Odvd(tc_Nat_Onat) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),f54(B,A,tc_Nat_Onat)))) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(A,C)).  [resolve(1694,a,1693,b)].
% 7.69/7.90  1695 class_Rings_Osemiring__0(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Osemiring__0) # label(axiom).  [assumption].
% 7.69/7.90  Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A).  [resolve(1695,a,1689,b)].
% 7.69/7.90  Derived: -class_Power_Opower(tc_RealDef_Oreal) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A).  [resolve(1695,a,1690,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_RealDef_Oreal) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C))) | c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,f53(B,A,tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1695,a,1691,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_RealDef_Oreal) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C))) | hBOOL(hAPP(A,f53(B,A,tc_RealDef_Oreal))).  [resolve(1695,a,1692,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_RealDef_Oreal) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),f54(B,A,tc_RealDef_Oreal)))) | -c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(A,C)).  [resolve(1695,a,1693,b)].
% 7.69/7.91  1696 class_Rings_Osemiring__0(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Osemiring__0) # label(axiom).  [assumption].
% 7.69/7.91  Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A).  [resolve(1696,a,1689,b)].
% 7.69/7.91  Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),A).  [resolve(1696,a,1690,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_Complex_Ocomplex) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C))) | c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,f53(B,A,tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).  [resolve(1696,a,1691,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_Complex_Ocomplex) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C))) | hBOOL(hAPP(A,f53(B,A,tc_Complex_Ocomplex))).  [resolve(1696,a,1692,b)].
% 7.69/7.91  Derived: -class_Rings_Odvd(tc_Complex_Ocomplex) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B),f54(B,A,tc_Complex_Ocomplex)))) | -c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,B,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,C,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | -hBOOL(hAPP(A,C)).  [resolve(1696,a,1693,b)].
% 7.69/7.91  1697 -class_Rings_Ocomm__semiring__0(A) | class_Rings_Osemiring__0(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Osemiring__0) # label(axiom).  [clausify(1023)].
% 7.69/7.91  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B).  [resolve(1697,b,1689,b)].
% 7.69/7.91  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B).  [resolve(1697,b,1690,b)].
% 7.69/7.91  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Rings_Odvd(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),f53(C,B,tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))).  [resolve(1697,b,1691,b)].
% 7.69/7.91  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Rings_Odvd(tc_Polynomial_Opoly(A)) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))) | hBOOL(hAPP(B,f53(C,B,tc_Polynomial_Opoly(A)))).  [resolve(1697,b,1692,b)].
% 7.99/8.18  Derived: -class_Rings_Ocomm__semiring__0(A) | -class_Rings_Odvd(tc_Polynomial_Opoly(A)) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),f54(C,B,tc_Polynomial_Opoly(A))))) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) | -hBOOL(hAPP(B,D)).  [resolve(1697,b,1693,b)].
% 7.99/8.18  1698 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f23(B,A),f24(B,A)) # label(fact_decseq__def) # label(axiom).  [clausify(675)].
% 7.99/8.18  1699 -class_Orderings_Oorder(A) | -c_SEQ_Odecseq(A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)) # label(fact_decseq__def) # label(axiom).  [clausify(675)].
% 7.99/8.18  Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f23(B,A),f24(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)).  [resolve(1698,b,1699,b)].
% 7.99/8.18  1700 -class_Orderings_Oorder(A) | c_SEQ_Odecseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f24(B,A)),hAPP(B,f23(B,A))) # label(fact_decseq__def) # label(axiom).  [clausify(675)].
% 7.99/8.18  Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f24(B,A)),hAPP(B,f23(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,D),hAPP(B,C)).  [resolve(1700,b,1699,b)].
% 7.99/8.18  1701 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom).  [assumption].
% 7.99/8.18  1702 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__0) # label(axiom).  [clausify(682)].
% 7.99/8.18  1703 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__by__0) # label(axiom).  [clausify(683)].
% 7.99/8.18  1704 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,B,c_Groups_Oone__class_Oone(A)) = B # label(fact_div__by__1) # label(axiom).  [clausify(684)].
% 7.99/8.18  1705 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1) # label(axiom).  [clausify(685)].
% 7.99/8.18  1706 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult2) # label(axiom).  [clausify(686)].
% 7.99/8.18  1707 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = C # label(fact_div__mult__self1__is__id) # label(axiom).  [clausify(687)].
% 7.99/8.18  1708 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),B) = C # label(fact_div__mult__self2__is__id) # label(axiom).  [clausify(688)].
% 7.99/8.18  1709 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Groups_Ozero__class_Ozero(A) # label(fact_div__mult__mult1__if) # label(axiom).  [clausify(689)].
% 7.99/8.18  1710 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = c_Divides_Odiv__class_Odiv(A,C,D) # label(fact_div__mult__mult1__if) # label(axiom).  [clausify(689)].
% 7.99/8.18  1711 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,B,B) = c_Groups_Oone__class_Oone(A) # label(fact_div__self) # label(axiom).  [clausify(690)].
% 7.99/8.18  1712 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),B) = c_Groups_Oplus__class_Oplus(A,D,c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self2) # label(axiom).  [clausify(697)].
% 7.99/8.18  1713 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),B) = c_Groups_Oplus__class_Oplus(A,D,c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__self1) # label(axiom).  [clausify(698)].
% 7.99/8.18  1714 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,B,C),B) = c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self1) # label(axiom).  [clausify(699)].
% 7.99/8.18  1715 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,C,B),B) = c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self2) # label(axiom).  [clausify(700)].
% 7.99/8.18  1716 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__div__trivial) # label(axiom).  [clausify(707)].
% 7.99/8.18  1717 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Oone__class_Oone(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__by__1) # label(axiom).  [clausify(714)].
% 7.99/8.18  1718 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__self) # label(axiom).  [clausify(716)].
% 7.99/8.18  1719 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_mod__by__0) # label(axiom).  [clausify(717)].
% 7.99/8.18  1720 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__0) # label(axiom).  [clausify(718)].
% 7.99/8.18  1721 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom).  [clausify(720)].
% 7.99/8.18  1722 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom).  [clausify(721)].
% 7.99/8.18  1723 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom).  [clausify(722)].
% 7.99/8.18  1724 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom).  [clausify(723)].
% 7.99/8.18  1725 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) # label(fact_mod__mult__right__eq) # label(axiom).  [clausify(725)].
% 7.99/8.18  1726 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__left__eq) # label(axiom).  [clausify(726)].
% 7.99/8.18  1727 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__eq) # label(axiom).  [clausify(727)].
% 7.99/8.18  1728 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_mod__mult__mult1) # label(axiom).  [clausify(728)].
% 7.99/8.18  1729 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,D)),C) # label(fact_mod__mult__mult2) # label(axiom).  [clausify(729)].
% 7.99/8.18  1730 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_zmod__simps_I4_J) # label(axiom).  [clausify(730)].
% 7.99/8.18  1731 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E),C) # label(fact_mod__mult__cong) # label(axiom).  [clausify(731)].
% 7.99/8.18  1732 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,F),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,D,E),C) # label(fact_mod__add__cong) # label(axiom).  [clausify(735)].
% 7.99/8.18  1733 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_zmod__simps_I1_J) # label(axiom).  [clausify(736)].
% 7.99/8.18  1734 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_zmod__simps_I2_J) # label(axiom).  [clausify(737)].
% 7.99/8.18  1735 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__eq) # label(axiom).  [clausify(738)].
% 7.99/8.18  1736 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C) # label(fact_mod__add__left__eq) # label(axiom).  [clausify(739)].
% 7.99/8.18  1737 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D) # label(fact_mod__add__right__eq) # label(axiom).  [clausify(740)].
% 7.99/8.18  1738 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom).  [clausify(741)].
% 7.99/8.18  1739 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom).  [clausify(742)].
% 7.99/8.18  1740 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mod__trivial) # label(axiom).  [clausify(743)].
% 7.99/8.18  1741 -class_Divides_Osemiring__div(A) | c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C)) = B # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom).  [clausify(745)].
% 7.99/8.18  1742 -class_Divides_Osemiring__div(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Omod(A,C,B)) = C # label(fact_mod__div__equality2) # label(axiom).  [clausify(746)].
% 7.99/8.18  1743 -class_Divides_Osemiring__div(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C),c_Divides_Odiv__class_Omod(A,B,C)) = B # label(fact_mod__div__equality) # label(axiom).  [clausify(747)].
% 7.99/8.18  1744 -class_Divides_Osemiring__div(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Omod(A,C,B)),D) = c_Groups_Oplus__class_Oplus(A,C,D) # label(fact_div__mod__equality2) # label(axiom).  [clausify(748)].
% 7.99/8.18  1745 -class_Divides_Osemiring__div(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,B,C)),C),c_Divides_Odiv__class_Omod(A,B,C)),D) = c_Groups_Oplus__class_Oplus(A,B,D) # label(fact_div__mod__equality) # label(axiom).  [clausify(749)].
% 7.99/8.18  1746 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom).  [clausify(814)].
% 7.99/8.18  1747 -class_Divides_Osemiring__div(A) | c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom).  [clausify(814)].
% 7.99/8.18  1748 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__imp__mod__0) # label(axiom).  [clausify(815)].
% 7.99/8.18  1749 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D)) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Rings_Odvd__class_Odvd(A,B,C) # label(fact_dvd__mod__imp__dvd) # label(axiom).  [clausify(816)].
% 7.99/8.18  1750 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_dvd__mod) # label(axiom).  [clausify(817)].
% 7.99/8.18  1751 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,D,C),B) = c_Divides_Odiv__class_Omod(A,D,B) # label(fact_mod__mod__cancel) # label(axiom).  [clausify(818)].
% 7.99/8.18  1752 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,D,C)) | c_Rings_Odvd__class_Odvd(A,B,D) # label(fact_dvd__mod__iff) # label(axiom).  [clausify(819)].
% 7.99/8.18  1753 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,D,C)) | -c_Rings_Odvd__class_Odvd(A,B,D) # label(fact_dvd__mod__iff) # label(axiom).  [clausify(819)].
% 7.99/8.18  1754 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Divides_Odiv__class_Odiv(A,C,B)),D) # label(fact_div__power) # label(axiom).  [clausify(872)].
% 7.99/8.18  1755 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,D,E) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),c_Divides_Odiv__class_Odiv(A,E,D)) # label(fact_div__mult__div__if__dvd) # label(axiom).  [clausify(873)].
% 7.99/8.18  1756 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),D) # label(fact_dvd__div__mult) # label(axiom).  [clausify(874)].
% 7.99/8.18  1757 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(A,C,B)),B) = C # label(fact_dvd__div__mult__self) # label(axiom).  [clausify(875)].
% 7.99/8.18  1758 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),c_Divides_Odiv__class_Odiv(A,C,B)) # label(fact_div__mult__swap) # label(axiom).  [clausify(876)].
% 7.99/8.18  1759 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(A,C,B)) = C # label(fact_dvd__mult__div__cancel) # label(axiom).  [clausify(877)].
% 7.99/8.18  1760 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Divides_Odiv__class_Odiv(A,c_Groups_Oplus__class_Oplus(A,C,D),B) = c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Divides_Odiv__class_Odiv(A,D,B)) # label(fact_div__add) # label(axiom).  [clausify(878)].
% 7.99/8.18  1761 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,D) | -c_Rings_Odvd__class_Odvd(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Divides_Odiv__class_Odiv(A,D,B)) | c_Rings_Odvd__class_Odvd(A,C,D) # label(fact_div__dvd__div) # label(axiom).  [clausify(879)].
% 7.99/8.18  1762 -class_Divides_Osemiring__div(A) | -c_Rings_Odvd__class_Odvd(A,B,C) | -c_Rings_Odvd__class_Odvd(A,B,D) | c_Rings_Odvd__class_Odvd(A,c_Divides_Odiv__class_Odiv(A,C,B),c_Divides_Odiv__class_Odiv(A,D,B)) | -c_Rings_Odvd__class_Odvd(A,C,D) # label(fact_div__dvd__div) # label(axiom).  [clausify(879)].
% 7.99/8.18  1763 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Odiv(A,C,B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_dvd__div__eq__mult) # label(axiom).  [clausify(880)].
% 7.99/8.18  1764 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -c_Rings_Odvd__class_Odvd(A,B,C) | c_Divides_Odiv__class_Odiv(A,C,B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_dvd__div__eq__mult) # label(axiom).  [clausify(880)].
% 7.99/8.18  1765 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -c_Rings_Odvd__class_Odvd(A,B,D) | -c_Rings_Odvd__class_Odvd(A,C,E) | c_Divides_Odiv__class_Odiv(A,D,B) != c_Divides_Odiv__class_Odiv(A,E,C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) # label(fact_dvd__div__div__eq__mult) # label(axiom).  [clausify(881)].
% 7.99/8.18  1766 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -c_Rings_Odvd__class_Odvd(A,B,D) | -c_Rings_Odvd__class_Odvd(A,C,E) | c_Divides_Odiv__class_Odiv(A,D,B) = c_Divides_Odiv__class_Odiv(A,E,C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) # label(fact_dvd__div__div__eq__mult) # label(axiom).  [clausify(881)].
% 7.99/8.18  Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1702,a)].
% 7.99/8.18  Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1703,a)].
% 7.99/8.18  Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = A.  [resolve(1701,a,1704,a)].
% 7.99/8.18  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C).  [resolve(1701,a,1705,a)].
% 7.99/8.18  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,C).  [resolve(1701,a,1706,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = B.  [resolve(1701,a,1707,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A),A) = B.  [resolve(1701,a,1708,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1709,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,A) = c_Groups_Oone__class_Oone(tc_Int_Oint).  [resolve(1701,a,1711,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)).  [resolve(1701,a,1712,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)).  [resolve(1701,a,1713,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Oone__class_Oone(tc_Int_Oint)).  [resolve(1701,a,1714,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A),A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Groups_Oone__class_Oone(tc_Int_Oint)).  [resolve(1701,a,1715,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1716,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1717,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1718,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A.  [resolve(1701,a,1719,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1720,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B).  [resolve(1701,a,1721,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C).  [resolve(1701,a,1722,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1723,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1724,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C).  [resolve(1701,a,1725,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B).  [resolve(1701,a,1726,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B).  [resolve(1701,a,1727,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)).  [resolve(1701,a,1728,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C)),B).  [resolve(1701,a,1729,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D),B).  [resolve(1701,a,1731,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,E),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D),B).  [resolve(1701,a,1732,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B).  [resolve(1701,a,1733,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C).  [resolve(1701,a,1734,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),B).  [resolve(1701,a,1735,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A).  [resolve(1701,a,1738,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B).  [resolve(1701,a,1739,a)].
% 7.99/8.19  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B).  [resolve(1701,a,1740,a)].
% 7.99/8.19  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B)) = A.  [resolve(1701,a,1741,a)].
% 7.99/8.19  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)) = B.  [resolve(1701,a,1742,a)].
% 7.99/8.19  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)) = A.  [resolve(1701,a,1743,a)].
% 7.99/8.19  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C).  [resolve(1701,a,1744,a)].
% 7.99/8.19  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)),B),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C).  [resolve(1701,a,1745,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1746,a)].
% 7.99/8.19  Derived: c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1701,a,1747,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B).  [resolve(1701,a,1749,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)).  [resolve(1701,a,1750,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,C,A).  [resolve(1701,a,1751,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),C).  [resolve(1701,a,1754,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,C,D) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,C)).  [resolve(1701,a,1755,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),C).  [resolve(1701,a,1756,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)),A) = B.  [resolve(1701,a,1757,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)).  [resolve(1701,a,1758,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A)) = B.  [resolve(1701,a,1759,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C),A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A)).  [resolve(1701,a,1760,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A)) | c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C).  [resolve(1701,a,1761,a)].
% 7.99/8.19  Derived: -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A),c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A)) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C).  [resolve(1701,a,1762,a)].
% 7.99/8.19  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) = B.  [resolve(1701,a,1763,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) != B.  [resolve(1701,a,1764,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,D) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B).  [resolve(1701,a,1765,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C) | -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,D) | c_Divides_Odiv__class_Odiv(tc_Int_Oint,C,A) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B).  [resolve(1701,a,1766,a)].
% 7.99/8.20  1767 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom).  [assumption].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1702,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1703,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A.  [resolve(1767,a,1704,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C).  [resolve(1767,a,1705,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,C).  [resolve(1767,a,1706,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = B.  [resolve(1767,a,1707,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),A) = B.  [resolve(1767,a,1708,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1709,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,A) = c_Groups_Oone__class_Oone(tc_Nat_Onat).  [resolve(1767,a,1711,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)).  [resolve(1767,a,1712,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)).  [resolve(1767,a,1713,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).  [resolve(1767,a,1714,a)].
% 7.99/8.20  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A),A) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).  [resolve(1767,a,1715,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1716,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1717,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1718,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A.  [resolve(1767,a,1719,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1720,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B).  [resolve(1767,a,1721,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C).  [resolve(1767,a,1722,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1723,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1724,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),C).  [resolve(1767,a,1725,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B).  [resolve(1767,a,1726,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B).  [resolve(1767,a,1727,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)).  [resolve(1767,a,1728,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C)),B).  [resolve(1767,a,1729,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D),B).  [resolve(1767,a,1731,a)].
% 7.99/8.20  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,E),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D),B).  [resolve(1767,a,1732,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).  [resolve(1767,a,1733,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C).  [resolve(1767,a,1734,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).  [resolve(1767,a,1735,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A).  [resolve(1767,a,1738,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B).  [resolve(1767,a,1739,a)].
% 7.99/8.21  Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B).  [resolve(1767,a,1740,a)].
% 7.99/8.21  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B)) = A.  [resolve(1767,a,1741,a)].
% 7.99/8.21  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A)) = B.  [resolve(1767,a,1742,a)].
% 7.99/8.21  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)) = A.  [resolve(1767,a,1743,a)].
% 7.99/8.21  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A)),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C).  [resolve(1767,a,1744,a)].
% 7.99/8.21  Derived: c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,A,B)),B),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).  [resolve(1767,a,1745,a)].
% 7.99/8.21  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1746,a)].
% 7.99/8.21  Derived: c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat).  [resolve(1767,a,1747,a)].
% 7.99/8.21  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).  [resolve(1767,a,1749,a)].
% 7.99/8.21  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)).  [resolve(1767,a,1750,a)].
% 7.99/8.21  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,A).  [resolve(1767,a,1751,a)].
% 7.99/8.21  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),C).  [resolve(1767,a,1754,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,D) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,C)).  [resolve(1767,a,1755,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),C).  [resolve(1767,a,1756,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)),A) = B.  [resolve(1767,a,1757,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)).  [resolve(1767,a,1758,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A)) = B.  [resolve(1767,a,1759,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A)).  [resolve(1767,a,1760,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A)) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).  [resolve(1767,a,1761,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A)) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).  [resolve(1767,a,1762,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) = B.  [resolve(1767,a,1763,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) != B.  [resolve(1767,a,1764,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,D) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A) != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B).  [resolve(1767,a,1765,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C) | -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,D) | c_Divides_Odiv__class_Odiv(tc_Nat_Onat,C,A) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B).  [resolve(1767,a,1766,a)].
% 8.07/8.27  1768 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1451,a,1438,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1702,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1703,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = A.  [resolve(1768,a,1704,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C).  [resolve(1768,a,1705,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C).  [resolve(1768,a,1706,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = B.  [resolve(1768,a,1707,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),A),A) = B.  [resolve(1768,a,1708,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1709,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1711,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)).  [resolve(1768,a,1712,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)).  [resolve(1768,a,1713,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))).  [resolve(1768,a,1714,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))).  [resolve(1768,a,1715,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1716,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1717,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1718,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))) = A.  [resolve(1768,a,1719,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1720,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B).  [resolve(1768,a,1721,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C).  [resolve(1768,a,1722,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1723,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1724,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),C).  [resolve(1768,a,1725,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B).  [resolve(1768,a,1726,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C),B).  [resolve(1768,a,1727,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)).  [resolve(1768,a,1728,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C)),B).  [resolve(1768,a,1729,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),D),B).  [resolve(1768,a,1731,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,D),B).  [resolve(1768,a,1732,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C),B).  [resolve(1768,a,1733,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C).  [resolve(1768,a,1734,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C),B).  [resolve(1768,a,1735,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A).  [resolve(1768,a,1738,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B).  [resolve(1768,a,1739,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B).  [resolve(1768,a,1740,a)].
% 8.07/8.27  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B)) = A.  [resolve(1768,a,1741,a)].
% 8.07/8.27  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)) = B.  [resolve(1768,a,1742,a)].
% 8.07/8.27  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)) = A.  [resolve(1768,a,1743,a)].
% 8.07/8.27  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C).  [resolve(1768,a,1744,a)].
% 8.07/8.27  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B)),C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C).  [resolve(1768,a,1745,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1746,a)].
% 8.07/8.27  Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1768,a,1747,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B).  [resolve(1768,a,1749,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)).  [resolve(1768,a,1750,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A).  [resolve(1768,a,1751,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),C).  [resolve(1768,a,1754,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,C)).  [resolve(1768,a,1755,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),C).  [resolve(1768,a,1756,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)),A) = B.  [resolve(1768,a,1757,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)).  [resolve(1768,a,1758,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A)) = B.  [resolve(1768,a,1759,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A)).  [resolve(1768,a,1760,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C).  [resolve(1768,a,1761,a)].
% 8.07/8.27  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C).  [resolve(1768,a,1762,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A) = B.  [resolve(1768,a,1763,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),A) != B.  [resolve(1768,a,1764,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A) != c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B).  [resolve(1768,a,1765,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,A) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C),B).  [resolve(1768,a,1766,a)].
% 8.07/8.27  1769 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1451,a,1450,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1702,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1703,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = A.  [resolve(1769,a,1704,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C).  [resolve(1769,a,1705,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C).  [resolve(1769,a,1706,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = B.  [resolve(1769,a,1707,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),A),A) = B.  [resolve(1769,a,1708,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1709,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,A) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1711,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)).  [resolve(1769,a,1712,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A)),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)).  [resolve(1769,a,1713,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).  [resolve(1769,a,1714,a)].
% 8.07/8.27  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).  [resolve(1769,a,1715,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1716,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1717,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1718,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = A.  [resolve(1769,a,1719,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1720,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B).  [resolve(1769,a,1721,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C).  [resolve(1769,a,1722,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1723,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1724,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),C).  [resolve(1769,a,1725,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B).  [resolve(1769,a,1726,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C),B).  [resolve(1769,a,1727,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)).  [resolve(1769,a,1728,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C)),B).  [resolve(1769,a,1729,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),D),B).  [resolve(1769,a,1731,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,D),B).  [resolve(1769,a,1732,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B).  [resolve(1769,a,1733,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C).  [resolve(1769,a,1734,a)].
% 8.07/8.27  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B).  [resolve(1769,a,1735,a)].
% 8.07/8.28  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A).  [resolve(1769,a,1738,a)].
% 8.07/8.28  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B).  [resolve(1769,a,1739,a)].
% 8.07/8.28  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B).  [resolve(1769,a,1740,a)].
% 8.07/8.28  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B)) = A.  [resolve(1769,a,1741,a)].
% 8.07/8.28  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)) = B.  [resolve(1769,a,1742,a)].
% 8.07/8.28  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)) = A.  [resolve(1769,a,1743,a)].
% 8.07/8.28  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C).  [resolve(1769,a,1744,a)].
% 8.07/8.28  Derived: c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B)),C) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C).  [resolve(1769,a,1745,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1746,a)].
% 8.07/8.28  Derived: c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1769,a,1747,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B).  [resolve(1769,a,1749,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)).  [resolve(1769,a,1750,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B),A) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A).  [resolve(1769,a,1751,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),C).  [resolve(1769,a,1754,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,C)).  [resolve(1769,a,1755,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B),C),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),C).  [resolve(1769,a,1756,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)),A) = B.  [resolve(1769,a,1757,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)).  [resolve(1769,a,1758,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A)) = B.  [resolve(1769,a,1759,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C),A) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A)).  [resolve(1769,a,1760,a)].
% 8.07/8.28  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A)) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C).  [resolve(1769,a,1761,a)].
% 8.35/8.54  Derived: -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A)) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C).  [resolve(1769,a,1762,a)].
% 8.35/8.54  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A) = B.  [resolve(1769,a,1763,a)].
% 8.35/8.54  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),A) != B.  [resolve(1769,a,1764,a)].
% 8.35/8.54  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A) != c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B).  [resolve(1769,a,1765,a)].
% 8.35/8.54  Derived: c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C) | -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,D) | c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,A) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),D) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C),B).  [resolve(1769,a,1766,a)].
% 8.35/8.54  1770 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f49(B,A),f50(B,A)) # label(fact_incseq__def) # label(axiom).  [clausify(808)].
% 8.35/8.54  1771 -class_Orderings_Oorder(A) | -c_SEQ_Oincseq(A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)) # label(fact_incseq__def) # label(axiom).  [clausify(808)].
% 8.35/8.54  Derived: -class_Orderings_Oorder(A) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,f49(B,A),f50(B,A)) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)).  [resolve(1770,b,1771,b)].
% 8.35/8.54  1772 -class_Orderings_Oorder(A) | c_SEQ_Oincseq(A,B) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f49(B,A)),hAPP(B,f50(B,A))) # label(fact_incseq__def) # label(axiom).  [clausify(808)].
% 8.35/8.54  Derived: -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(A,hAPP(B,f49(B,A)),hAPP(B,f50(B,A))) | -class_Orderings_Oorder(A) | -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D) | c_Orderings_Oord__class_Oless__eq(A,hAPP(B,C),hAPP(B,D)).  [resolve(1772,b,1771,b)].
% 8.35/8.54  1773 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom).  [assumption].
% 8.35/8.54  1774 -class_Rings_Oring__1(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A))) # label(fact_real__squared__diff__one__factored) # label(axiom).  [clausify(923)].
% 8.49/8.69  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))).  [resolve(1773,a,1774,a)].
% 8.49/8.69  1775 class_Rings_Oring__1(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring__1) # label(axiom).  [assumption].
% 8.49/8.69  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).  [resolve(1775,a,1774,a)].
% 8.49/8.69  1776 class_Rings_Oring__1(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring__1) # label(axiom).  [assumption].
% 8.49/8.69  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))).  [resolve(1776,a,1774,a)].
% 8.49/8.69  1777 -class_Rings_Ocomm__ring__1(A) | class_Rings_Oring__1(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring__1) # label(axiom).  [clausify(1032)].
% 8.49/8.69  Derived: -class_Rings_Ocomm__ring__1(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))).  [resolve(1777,b,1774,a)].
% 8.49/8.69  1778 class_Divides_Oring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Oring__div) # label(axiom).  [assumption].
% 8.49/8.69  1779 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,F),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,D,E),C) # label(fact_mod__diff__cong) # label(axiom).  [clausify(932)].
% 8.49/8.69  1780 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__eq) # label(axiom).  [clausify(935)].
% 8.49/8.69  1781 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,D),C) # label(fact_mod__diff__left__eq) # label(axiom).  [clausify(936)].
% 8.49/8.69  1782 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,c_Groups_Ominus__class_Ominus(A,B,C),D) # label(fact_mod__diff__right__eq) # label(axiom).  [clausify(937)].
% 8.49/8.69  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,E),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D),B).  [resolve(1778,a,1779,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C),B).  [resolve(1778,a,1780,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C),B).  [resolve(1778,a,1781,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),C).  [resolve(1778,a,1782,a)].
% 8.54/8.74  1783 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)).  [resolve(1452,a,1438,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,D),B).  [resolve(1783,a,1779,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C),B).  [resolve(1783,a,1780,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,C),B).  [resolve(1783,a,1781,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_RealDef_Oreal),A,B),C).  [resolve(1783,a,1782,a)].
% 8.54/8.74  1784 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).  [resolve(1452,a,1450,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),D,B) != c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),E,B) | c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,E),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,D),B).  [resolve(1784,a,1779,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),C,B)),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B).  [resolve(1784,a,1780,a)].
% 8.54/8.74  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C),B) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,C),B).  [resolve(1784,a,1781,a)].
% 8.67/8.85  Derived: c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),B,C)),C) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),A,B),C).  [resolve(1784,a,1782,a)].
% 8.67/8.85  1785 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
% 8.67/8.85  1786 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom).  [clausify(939)].
% 8.67/8.85  1787 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,D,E) # label(fact_diff__eq__diff__less) # label(axiom).  [clausify(939)].
% 8.67/8.85  1788 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless(A,B,C) | c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom).  [clausify(964)].
% 8.67/8.85  1789 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless(A,B,C) | -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_less__iff__diff__less__0) # label(axiom).  [clausify(964)].
% 8.67/8.85  1790 -class_Groups_Oordered__ab__group__add(A) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom).  [clausify(965)].
% 8.67/8.85  1791 -class_Groups_Oordered__ab__group__add(A) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)) # label(fact_le__iff__diff__le__0) # label(axiom).  [clausify(965)].
% 8.67/8.85  1792 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | -c_Orderings_Oord__class_Oless__eq(A,B,C) | c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom).  [clausify(966)].
% 8.67/8.85  1793 -class_Groups_Oordered__ab__group__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ominus__class_Ominus(A,D,E) | c_Orderings_Oord__class_Oless__eq(A,B,C) | -c_Orderings_Oord__class_Oless__eq(A,D,E) # label(fact_diff__eq__diff__less__eq) # label(axiom).  [clausify(966)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D).  [resolve(1785,a,1786,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,D).  [resolve(1785,a,1787,a)].
% 8.67/8.85  Derived: -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1785,a,1788,a)].
% 8.67/8.85  Derived: c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1785,a,1789,a)].
% 8.67/8.85  Derived: -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1785,a,1790,a)].
% 8.67/8.85  Derived: c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).  [resolve(1785,a,1791,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D).  [resolve(1785,a,1792,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ominus__class_Ominus(tc_Int_Oint,C,D) | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,C,D).  [resolve(1785,a,1793,a)].
% 8.67/8.85  1794 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Oordered__ab__group__add) # label(axiom).  [assumption].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D).  [resolve(1794,a,1786,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C,D).  [resolve(1794,a,1787,a)].
% 8.67/8.85  Derived: -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1794,a,1788,a)].
% 8.67/8.85  Derived: c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1794,a,1789,a)].
% 8.67/8.85  Derived: -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1794,a,1790,a)].
% 8.67/8.85  Derived: c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(1794,a,1791,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D).  [resolve(1794,a,1792,a)].
% 8.67/8.85  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,C,D) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B) | -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,C,D).  [resolve(1794,a,1793,a)].
% 8.67/8.85  1795 -class_Rings_Olinordered__idom(A) | class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) # label(axiom).  [clausify(998)].
% 8.67/8.85  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E).  [resolve(1795,b,1786,a)].
% 8.67/8.85  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),D,E).  [resolve(1795,b,1787,a)].
% 8.67/8.85  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1795,b,1788,a)].
% 8.67/8.85  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1795,b,1789,a)].
% 8.82/9.02  Derived: -class_Rings_Olinordered__idom(A) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1795,b,1790,a)].
% 8.82/9.02  Derived: -class_Rings_Olinordered__idom(A) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).  [resolve(1795,b,1791,a)].
% 8.82/9.02  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E).  [resolve(1795,b,1792,a)].
% 8.82/9.02  Derived: -class_Rings_Olinordered__idom(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E) | c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),B,C) | -c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(A),D,E).  [resolve(1795,b,1793,a)].
% 8.82/9.02  1796 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom).  [assumption].
% 8.82/9.02  1797 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) != c_Groups_Ozero__class_Ozero(A) | B = C # label(fact_right__minus__eq) # label(axiom).  [clausify(940)].
% 8.82/9.02  1798 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,C) = c_Groups_Ozero__class_Ozero(A) | B != C # label(fact_right__minus__eq) # label(axiom).  [clausify(940)].
% 8.82/9.02  1799 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_diff__self) # label(axiom).  [clausify(942)].
% 8.82/9.02  1800 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom).  [clausify(943)].
% 8.82/9.02  1801 -class_Groups_Ogroup__add(A) | c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C) = B # label(fact_add__diff__cancel) # label(axiom).  [clausify(968)].
% 8.82/9.02  1802 -class_Groups_Ogroup__add(A) | c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C) = B # label(fact_diff__add__cancel) # label(axiom).  [clausify(969)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | A = B.  [resolve(1796,a,1797,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | A != B.  [resolve(1796,a,1798,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint).  [resolve(1796,a,1799,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A.  [resolve(1796,a,1800,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),B) = A.  [resolve(1796,a,1801,a)].
% 8.82/9.02  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,B),B) = A.  [resolve(1796,a,1802,a)].
% 8.82/9.02  1803 class_Groups_Ogroup__add(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Groups_Ogroup__add) # label(axiom).  [assumption].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B.  [resolve(1803,a,1797,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) | A != B.  [resolve(1803,a,1798,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,A) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1803,a,1799,a)].
% 8.82/9.02  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = A.  [resolve(1803,a,1800,a)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),B) = A.  [resolve(1803,a,1801,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),B) = A.  [resolve(1803,a,1802,a)].
% 8.97/9.18  1804 class_Groups_Ogroup__add(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Groups_Ogroup__add) # label(axiom).  [assumption].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B.  [resolve(1804,a,1797,a)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) | A != B.  [resolve(1804,a,1798,a)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,A) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(1804,a,1799,a)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A.  [resolve(1804,a,1800,a)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,A,B),B) = A.  [resolve(1804,a,1801,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,B),B) = A.  [resolve(1804,a,1802,a)].
% 8.97/9.18  1805 -class_Groups_Oab__group__add(A) | class_Groups_Ogroup__add(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Groups_Ogroup__add) # label(axiom).  [clausify(1024)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C.  [resolve(1805,b,1797,a)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B != C.  [resolve(1805,b,1798,a)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,B) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).  [resolve(1805,b,1799,a)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B.  [resolve(1805,b,1800,a)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),C) = B.  [resolve(1805,b,1801,a)].
% 8.97/9.18  Derived: -class_Groups_Oab__group__add(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C),C) = B.  [resolve(1805,b,1802,a)].
% 8.97/9.18  1806 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom).  [assumption].
% 8.97/9.18  1807 -class_Rings_Oring(A) | c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,D)),E)) # label(fact_mult__diff__mult) # label(axiom).  [clausify(961)].
% 8.97/9.18  1808 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D) = F # label(fact_eq__add__iff1) # label(axiom).  [clausify(962)].
% 8.97/9.18  1809 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D) != F # label(fact_eq__add__iff1) # label(axiom).  [clausify(962)].
% 8.97/9.18  1810 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) != c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F) = D # label(fact_eq__add__iff2) # label(axiom).  [clausify(963)].
% 8.97/9.18  1811 -class_Rings_Oring(A) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F) | c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F) != D # label(fact_eq__add__iff2) # label(axiom).  [clausify(963)].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ominus__class_Ominus(tc_Int_Oint,B,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,C)),D)).  [resolve(1806,a,1807,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C) = E.  [resolve(1806,a,1808,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,A,D)),B),C) != E.  [resolve(1806,a,1809,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E) = C.  [resolve(1806,a,1810,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,D,A)),B),E) != C.  [resolve(1806,a,1811,a)].
% 8.97/9.18  1812 class_Rings_Oring(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__Rings_Oring) # label(axiom).  [assumption].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C)),D)).  [resolve(1812,a,1807,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C) = E.  [resolve(1812,a,1808,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,D)),B),C) != E.  [resolve(1812,a,1809,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E) = C.  [resolve(1812,a,1810,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),B),E) | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,D,A)),B),E) != C.  [resolve(1812,a,1811,a)].
% 8.97/9.18  1813 class_Rings_Oring(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__Rings_Oring) # label(axiom).  [assumption].
% 8.97/9.18  Derived: c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C)),D)).  [resolve(1813,a,1807,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D)),B),C) = E.  [resolve(1813,a,1808,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,D)),B),C) != E.  [resolve(1813,a,1809,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A)),B),E) = C.  [resolve(1813,a,1810,a)].
% 8.97/9.18  Derived: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E) | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,D,A)),B),E) != C.  [resolve(1813,a,1811,a)].
% 8.97/9.18  1814 -class_Rings_Ocomm__ring(A) | class_Rings_Oring(tc_Polynomial_Opoly(A)) # label(arity_Polynomial__Opoly__Rings_Oring) # label(axiom).  [clausify(1035)].
% 8.97/9.18  Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),C,E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,D)),E)).  [resolve(1814,b,1807,a)].
% 8.97/9.18  Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D) = F.  [resolve(1814,b,1808,a)].
% 9.14/9.35  Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,E)),C),D) != F.  [resolve(1814,b,1809,a)].
% 9.14/9.35  Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F) = D.  [resolve(1814,b,1810,a)].
% 9.14/9.35  Derived: -class_Rings_Ocomm__ring(A) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),D) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),E),C),F) | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),E,B)),C),F) != D.  [resolve(1814,b,1811,a)].
% 9.14/9.35  1815 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(arity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom).  [assumption].
% 9.14/9.35  1816 -class_RealVector_Oreal__field(A) | c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)),F) = c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,C,E),F)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Odivide(A,c_Groups_Ominus__class_Ominus(A,B,D),F)),E)) # label(fact_DERIV__mult__lemma) # label(axiom).  [clausify(975)].
% 9.14/9.35  Derived: c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)),E) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,D),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,C),E)),D)).  [resolve(1815,a,1816,a)].
% 9.14/9.35  1817 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(arity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom).  [assumption].
% 9.14/9.35  Derived: c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)),E) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B,D),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,A,C),E)),D)).  [resolve(1817,a,1816,a)].
% 15.00/15.24  
% 15.00/15.24  ============================== end predicate elimination =============
% 15.00/15.24  
% 15.00/15.24  Auto_denials:  (non-Horn, no changes).
% 15.00/15.24  
% 15.00/15.24  Term ordering decisions:
% 15.00/15.24  Function symbol KB weights:  tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_Nat_Onat=1. tc_Complex_Ocomplex=1. v_c____=1. v_cs____=1. v_aa____=1. v_da____=1. v_z____=1. tc_HOL_Obool=1. v_p=1. c1=1. hAPP=1. c_Groups_Oabs__class_Oabs=1. c_RealVector_Onorm__class_Onorm=1. c_NthRoot_Oroot=1. c_RealDef_Oreal=1. c_Polynomial_Opoly=1. tc_fun=1. c_fequal=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. f1=1. f3=1. f4=1. f5=1. f6=1. f8=1. f9=1. f10=1. f11=1. f13=1. f14=1. f15=1. f16=1. f18=1. f21=1. f22=1. f23=1. f24=1. f25=1. f28=1. f29=1. f31=1. f39=1. f40=1. f49=1. f50=1. c_Groups_Ozero__class_Ozero=1. tc_Polynomial_Opoly=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oone__class_Oone=1. c_Power_Opower__class_Opower=1. c_RComplete_Onatfloor=1. c_RComplete_Onatceiling=1. f7=1. f12=1. f17=1. c_Groups_Oplus__class_Oplus=1. c_Divides_Odiv__class_Omod=1. c_Divides_Odiv__class_Odiv=1. c_Groups_Ominus__class_Ominus=1. c_Rings_Oinverse__class_Odivide=1. c_Polynomial_OpCons=1. c_Polynomial_Opcompose=1. c_Polynomial_Oorder=1. c_Power_Opower_Opower=1. f19=1. f20=1. f26=1. f27=1. f30=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f38=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f52=1. f53=1. f54=1. f55=1. c_If=1. f2=1. f51=1. f56=1. c_Polynomial_Opoly__rec=1.
% 15.00/15.24  
% 15.00/15.24  ============================== end of process initial clauses ========
% 15.00/15.24  
% 15.00/15.24  ============================== CLAUSES FOR SEARCH ====================
% 15.00/15.24  
% 15.00/15.24  ============================== end of clauses for search =============
% 15.00/15.24  
% 15.00/15.24  ============================== SEARCH ================================
% 15.00/15.24  
% 15.00/15.24  % Starting search at 8.24 seconds.
% 15.00/15.24  
% 15.00/15.24  Low Water (keep): wt=65.000, iters=3653
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% 15.00/15.24  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 120 (0.00 of 8.59 sec).
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% 15.00/15.24  Low Water (keep): wt=37.000, iters=3345
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% 15.00/15.24  Low Water (keep): wt=35.000, iters=3367
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% 15.00/15.24  Low Water (keep): wt=34.000, iters=3360
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% 15.00/15.24  Low Water (keep): wt=33.000, iters=3358
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% 15.00/15.24  Low Water (keep): wt=32.000, iters=3388
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% 15.00/15.24  Low Water (keep): wt=31.000, iters=3333
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% 15.00/15.24  Low Water (keep): wt=28.000, iters=3342
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% 15.00/15.24  Low Water (keep): wt=26.000, iters=3334
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% 15.00/15.24  Low Water (keep): wt=23.000, iters=3333
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% 15.00/15.24  Low Water (keep): wt=22.000, iters=3353
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% 15.00/15.24  Low Water (keep): wt=21.000, iters=3335
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% 15.00/15.24  Low Water (displace): id=6196, wt=87.000
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% 15.00/15.24  Low Water (displace): id=6607, wt=71.000
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% 15.00/15.24  Low Water (displace): id=6645, wt=70.000
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% 15.00/15.24  Low Water (displace): id=6197, wt=64.000
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% 15.00/15.24  Low Water (displace): id=6629, wt=58.000
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% 15.00/15.24  Low Water (displace): id=6575, wt=57.000
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% 15.00/15.24  Low Water (displace): id=6667, wt=56.000
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% 15.00/15.24  Low Water (displace): id=17209, wt=12.000
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% 15.00/15.24  Low Water (displace): id=17944, wt=11.000
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% 15.00/15.24  Low Water (displace): id=18946, wt=10.000
% 15.00/15.24  
% 15.00/15.24  Low Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------