TSTP Solution File: SWV609-1 by Prover9---1109a

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWV609-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n003.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 : Wed Jul 20 21:14:05 EDT 2022

% Result   : Timeout 300.03s 300.30s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem  : SWV609-1 : TPTP v8.1.0. Released v4.1.0.
% 0.14/0.15  % Command  : tptp2X_and_run_prover9 %d %s
% 0.15/0.37  % Computer : n003.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Wed Jun 15 20:29:26 EDT 2022
% 0.15/0.38  % CPUTime  : 
% 1.56/1.80  ============================== Prover9 ===============================
% 1.56/1.80  Prover9 (32) version 2009-11A, November 2009.
% 1.56/1.80  Process 22999 was started by sandbox on n003.cluster.edu,
% 1.56/1.80  Wed Jun 15 20:29:27 2022
% 1.56/1.80  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22846_n003.cluster.edu".
% 1.56/1.80  ============================== end of head ===========================
% 1.56/1.80  
% 1.56/1.80  ============================== INPUT =================================
% 1.56/1.80  
% 1.56/1.80  % Reading from file /tmp/Prover9_22846_n003.cluster.edu
% 1.56/1.80  
% 1.56/1.80  set(prolog_style_variables).
% 1.56/1.80  set(auto2).
% 1.56/1.80      % set(auto2) -> set(auto).
% 1.56/1.80      % set(auto) -> set(auto_inference).
% 1.56/1.80      % set(auto) -> set(auto_setup).
% 1.56/1.80      % set(auto_setup) -> set(predicate_elim).
% 1.56/1.80      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.56/1.80      % set(auto) -> set(auto_limits).
% 1.56/1.80      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.56/1.80      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.56/1.80      % set(auto) -> set(auto_denials).
% 1.56/1.80      % set(auto) -> set(auto_process).
% 1.56/1.80      % set(auto2) -> assign(new_constants, 1).
% 1.56/1.80      % set(auto2) -> assign(fold_denial_max, 3).
% 1.56/1.80      % set(auto2) -> assign(max_weight, "200.000").
% 1.56/1.80      % set(auto2) -> assign(max_hours, 1).
% 1.56/1.80      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.56/1.80      % set(auto2) -> assign(max_seconds, 0).
% 1.56/1.80      % set(auto2) -> assign(max_minutes, 5).
% 1.56/1.80      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.56/1.80      % set(auto2) -> set(sort_initial_sos).
% 1.56/1.80      % set(auto2) -> assign(sos_limit, -1).
% 1.56/1.80      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.56/1.80      % set(auto2) -> assign(max_megs, 400).
% 1.56/1.80      % set(auto2) -> assign(stats, some).
% 1.56/1.80      % set(auto2) -> clear(echo_input).
% 1.56/1.80      % set(auto2) -> set(quiet).
% 1.56/1.80      % set(auto2) -> clear(print_initial_clauses).
% 1.56/1.80      % set(auto2) -> clear(print_given).
% 1.56/1.80  assign(lrs_ticks,-1).
% 1.56/1.80  assign(sos_limit,10000).
% 1.56/1.80  assign(order,kbo).
% 1.56/1.80  set(lex_order_vars).
% 1.56/1.80  clear(print_given).
% 1.56/1.80  
% 1.56/1.80  % formulas(sos).  % not echoed (1402 formulas)
% 1.56/1.80  
% 1.56/1.80  ============================== end of input ==========================
% 1.56/1.80  
% 1.56/1.80  % From the command line: assign(max_seconds, 300).
% 1.56/1.80  
% 1.56/1.80  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.56/1.80  
% 1.56/1.80  % Formulas that are not ordinary clauses:
% 1.56/1.80  
% 1.56/1.80  ============================== end of process non-clausal formulas ===
% 1.56/1.80  
% 1.56/1.80  ============================== PROCESS INITIAL CLAUSES ===============
% 1.56/1.80  
% 1.56/1.80  ============================== PREDICATE ELIMINATION =================
% 1.56/1.80  1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom).  [assumption].
% 1.56/1.80  2 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom).  [assumption].
% 1.56/1.80  3 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A))) # label(cls_less__add__one_0) # label(axiom).  [assumption].
% 1.56/1.80  4 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom).  [assumption].
% 1.56/1.80  5 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom).  [assumption].
% 1.56/1.80  6 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom).  [assumption].
% 1.56/1.80  7 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  8 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom).  [assumption].
% 1.56/1.80  9 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A))) # label(cls_zero__less__two_0) # label(axiom).  [assumption].
% 1.56/1.80  10 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom).  [assumption].
% 1.56/1.80  11 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) # label(cls_of__nat__le__iff_1) # label(axiom).  [assumption].
% 1.56/1.80  12 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  13 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom).  [assumption].
% 1.56/1.80  14 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom).  [assumption].
% 1.56/1.80  15 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom).  [assumption].
% 1.56/1.80  16 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom).  [assumption].
% 1.56/1.80  17 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom).  [assumption].
% 1.56/1.80  18 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom).  [assumption].
% 1.56/1.80  19 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom).  [assumption].
% 1.56/1.80  20 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  21 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom).  [assumption].
% 1.56/1.80  22 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  23 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom).  [assumption].
% 1.56/1.80  24 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom).  [assumption].
% 1.56/1.80  25 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom).  [assumption].
% 1.56/1.80  26 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom).  [assumption].
% 1.56/1.80  27 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  28 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom).  [assumption].
% 1.56/1.80  29 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom).  [assumption].
% 1.56/1.80  30 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  31 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom).  [assumption].
% 1.56/1.80  32 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != hAPP(c_Power_Opower__class_Opower(B,A),D) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom).  [assumption].
% 1.56/1.80  33 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,D)),A),hAPP(c_Power_Opower__class_Opower(C,A),hAPP(c_Suc,D)))) # label(cls_power__le__imp__le__base_0) # label(axiom).  [assumption].
% 1.56/1.80  34 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) != hAPP(c_Power_Opower__class_Opower(D,A),hAPP(c_Suc,C)) | B = D | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom).  [assumption].
% 1.56/1.80  35 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),D),A),hAPP(c_Power_Opower__class_Opower(C,A),D))) # label(cls_power__less__imp__less__base_0) # label(axiom).  [assumption].
% 1.56/1.80  36 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom).  [assumption].
% 1.56/1.80  37 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom).  [assumption].
% 1.56/1.80  38 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom).  [assumption].
% 1.56/1.80  39 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom).  [assumption].
% 1.56/1.80  40 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom).  [assumption].
% 1.56/1.80  41 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != hAPP(c_Power_Opower__class_Opower(D,A),C) | B = D | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom).  [assumption].
% 1.56/1.80  42 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom).  [assumption].
% 1.56/1.80  43 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom).  [assumption].
% 1.56/1.80  44 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom).  [assumption].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(1,a,2,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))).  [resolve(1,a,3,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,4,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,5,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,tc_nat),A),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)).  [resolve(1,a,6,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,8,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))).  [resolve(1,a,9,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,10,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(1,a,11,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))).  [resolve(1,a,12,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(1,a,13,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,14,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,15,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,16,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(1,a,17,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)).  [resolve(1,a,18,a)].
% 1.56/1.80  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(1,a,19,a)].
% 1.56/1.80  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(1,a,20,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))).  [resolve(1,a,21,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,23,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))).  [resolve(1,a,24,a)].
% 1.56/1.80  Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(1,a,25,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)).  [resolve(1,a,26,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))).  [resolve(1,a,27,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)).  [resolve(1,a,28,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))).  [resolve(1,a,29,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))).  [resolve(1,a,30,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,31,a)].
% 1.56/1.80  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != hAPP(c_Power_Opower__class_Opower(A,tc_nat),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C.  [resolve(1,a,32,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,C)),tc_nat),hAPP(c_Power_Opower__class_Opower(B,tc_nat),hAPP(c_Suc,C)))).  [resolve(1,a,33,a)].
% 1.56/1.80  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)) != hAPP(c_Power_Opower__class_Opower(C,tc_nat),hAPP(c_Suc,B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,34,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),C),tc_nat),hAPP(c_Power_Opower__class_Opower(B,tc_nat),C))).  [resolve(1,a,35,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(1,a,36,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,tc_nat),A),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)).  [resolve(1,a,37,a)].
% 1.56/1.80  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(1,a,38,a)].
% 1.56/1.81  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != hAPP(c_Power_Opower__class_Opower(C,tc_nat),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,41,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,42,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(1,a,43,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(1,a,44,a)].
% 1.56/1.81  45 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom).  [assumption].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(45,a,2,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint))).  [resolve(45,a,3,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,4,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,5,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)).  [resolve(45,a,6,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,8,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint))).  [resolve(45,a,9,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,10,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(45,a,11,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))).  [resolve(45,a,12,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(45,a,13,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,14,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,15,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,16,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(45,a,17,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)).  [resolve(45,a,18,a)].
% 1.56/1.81  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(45,a,19,a)].
% 1.56/1.81  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(45,a,20,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))).  [resolve(45,a,21,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,23,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))).  [resolve(45,a,24,a)].
% 1.56/1.81  Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(45,a,25,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,26,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))).  [resolve(45,a,27,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)).  [resolve(45,a,28,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))).  [resolve(45,a,29,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))).  [resolve(45,a,30,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(45,a,31,a)].
% 1.56/1.81  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | B = C.  [resolve(45,a,32,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,C)),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),hAPP(c_Suc,C)))).  [resolve(45,a,33,a)].
% 1.56/1.81  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)) != hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),hAPP(c_Suc,B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,34,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),C))).  [resolve(45,a,35,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(45,a,36,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)).  [resolve(45,a,37,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(45,a,38,a)].
% 1.56/1.81  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,41,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,42,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(45,a,43,a)].
% 1.56/1.81  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(45,a,44,a)].
% 1.66/1.91  46 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom).  [assumption].
% 1.66/1.91  47 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),C,A) # label(cls_dvd__mult__right_0) # label(axiom).  [assumption].
% 1.66/1.91  48 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),C,A) # label(cls_dvd__mult__left_0) # label(axiom).  [assumption].
% 1.66/1.91  49 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult2_0) # label(axiom).  [assumption].
% 1.66/1.91  50 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult_0) # label(axiom).  [assumption].
% 1.66/1.91  51 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__dvd_0) # label(axiom).  [assumption].
% 1.66/1.91  52 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom).  [assumption].
% 1.66/1.91  53 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom).  [assumption].
% 1.66/1.91  54 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom).  [assumption].
% 1.66/1.91  55 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom).  [assumption].
% 1.66/1.91  56 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Omul__a_0) # label(axiom).  [assumption].
% 1.66/1.91  57 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),D) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom).  [assumption].
% 1.66/1.91  58 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_class__semiring_Omul__d_0) # label(axiom).  [assumption].
% 1.66/1.91  59 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__trans_0) # label(axiom).  [assumption].
% 1.66/1.91  60 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,B,A) # label(cls_dvd__refl_0) # label(axiom).  [assumption].
% 1.66/1.91  61 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(D,A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom).  [assumption].
% 1.66/1.91  62 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom).  [assumption].
% 1.66/1.91  63 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom).  [assumption].
% 1.66/1.91  64 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D)) = hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oplus__class_Oplus(C,D,tc_nat)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom).  [assumption].
% 1.66/1.91  65 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),A),B),A) # label(cls_dvd__power_1) # label(axiom).  [assumption].
% 1.66/1.91  66 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),A),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom).  [assumption].
% 1.66/1.91  67 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__add_0) # label(axiom).  [assumption].
% 1.66/1.91  68 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom).  [assumption].
% 1.66/1.91  69 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),A),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom).  [assumption].
% 1.66/1.91  70 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom).  [assumption].
% 1.66/1.91  71 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),A),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom).  [assumption].
% 1.66/1.91  72 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A) # label(cls_dvd__triv__right_0) # label(axiom).  [assumption].
% 1.66/1.91  73 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_dvd__triv__left_0) # label(axiom).  [assumption].
% 1.66/1.91  74 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom).  [assumption].
% 1.66/1.91  75 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom).  [assumption].
% 1.66/1.91  76 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Omul__c_0) # label(axiom).  [assumption].
% 1.66/1.91  77 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom).  [assumption].
% 1.66/1.91  78 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom).  [assumption].
% 1.66/1.91  79 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom).  [assumption].
% 1.66/1.91  80 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom).  [assumption].
% 1.66/1.91  81 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom).  [assumption].
% 1.66/1.91  82 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom).  [assumption].
% 1.66/1.91  83 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(B,A),C),hAPP(c_Power_Opower__class_Opower(B,A),D),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_le__imp__power__dvd_0) # label(axiom).  [assumption].
% 1.66/1.91  84 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom).  [assumption].
% 1.66/1.91  85 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Oadd__c_0) # label(axiom).  [assumption].
% 1.66/1.91  86 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,B,A) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom).  [assumption].
% 1.66/1.91  87 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom).  [assumption].
% 1.66/1.91  88 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(C,c_HOL_Oone__class_Oone(A),A),A),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom).  [assumption].
% 1.66/1.91  89 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom).  [assumption].
% 1.66/1.91  90 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(B,A),C),A),B) = hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom).  [assumption].
% 1.66/1.91  91 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(B,A),C),hAPP(c_Power_Opower__class_Opower(D,A),E),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__le_0) # label(axiom).  [assumption].
% 1.66/1.91  92 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom).  [assumption].
% 1.66/1.91  93 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom).  [assumption].
% 1.66/1.91  94 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom).  [assumption].
% 1.66/1.91  95 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_dvd__0__right_0) # label(axiom).  [assumption].
% 1.66/1.91  96 -class_Ring__and__Field_Ocomm__semiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_dvd__0__left_0) # label(axiom).  [assumption].
% 1.66/1.91  97 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom).  [assumption].
% 1.66/1.91  98 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom).  [assumption].
% 1.66/1.91  99 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom).  [assumption].
% 1.66/1.91  100 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,E,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_mult__dvd__mono_0) # label(axiom).  [assumption].
% 1.66/1.91  101 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(B,A),C),D,A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(B,A),E),D,A) # label(cls_power__le__dvd_0) # label(axiom).  [assumption].
% 1.66/1.91  102 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_Power_Opower__class_Opower(B,A),C),A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_dvd__power_0) # label(axiom).  [assumption].
% 1.66/1.91  103 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom).  [assumption].
% 1.66/1.91  104 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(B,A),D),A),hAPP(c_Power_Opower__class_Opower(C,A),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom).  [assumption].
% 1.66/1.91  105 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),D) = hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom).  [assumption].
% 1.66/1.91  106 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(B,A),C),hAPP(c_Power_Opower__class_Opower(D,A),C),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__same_0) # label(axiom).  [assumption].
% 1.66/1.91  107 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom).  [assumption].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),B,tc_nat).  [resolve(46,a,47,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),B,tc_nat).  [resolve(46,a,48,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).  [resolve(46,a,49,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).  [resolve(46,a,50,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).  [resolve(46,a,51,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),B).  [resolve(46,a,52,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)).  [resolve(46,a,53,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C).  [resolve(46,a,54,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)).  [resolve(46,a,55,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),C) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),tc_nat).  [resolve(46,a,57,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat).  [resolve(46,a,58,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).  [resolve(46,a,59,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat).  [resolve(46,a,60,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),D)).  [resolve(46,a,63,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat)).  [resolve(46,a,64,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat),B).  [resolve(46,a,66,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).  [resolve(46,a,67,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,D,tc_nat),tc_nat).  [resolve(46,a,68,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A) = A.  [resolve(46,a,69,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat)) = A.  [resolve(46,a,70,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A),tc_nat).  [resolve(46,a,72,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat).  [resolve(46,a,73,a)].
% 1.66/1.91  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)).  [resolve(46,a,74,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A).  [resolve(46,a,76,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat).  [resolve(46,a,78,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat).  [resolve(46,a,80,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat).  [resolve(46,a,81,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat).  [resolve(46,a,82,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C),tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(46,a,83,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat).  [resolve(46,a,84,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,A,tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),A).  [resolve(46,a,86,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),B,tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),B).  [resolve(46,a,87,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),A).  [resolve(46,a,88,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)).  [resolve(46,a,89,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),A) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_Suc,B)).  [resolve(46,a,90,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),hAPP(c_Power_Opower__class_Opower(C,tc_nat),D),tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).  [resolve(46,a,91,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(46,a,92,a)].
% 1.66/1.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(46,a,93,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).  [resolve(46,a,95,a)].
% 1.66/1.91  Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).  [resolve(46,a,96,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A.  [resolve(46,a,97,a)].
% 1.66/1.91  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A.  [resolve(46,a,98,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).  [resolve(46,a,100,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),C,tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_nat),D),C,tc_nat).  [resolve(46,a,101,a)].
% 1.66/1.91  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(46,a,102,a)].
% 1.66/1.91  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat)) = A.  [resolve(46,a,103,a)].
% 1.66/1.91  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_nat),C),tc_nat),hAPP(c_Power_Opower__class_Opower(B,tc_nat),C)).  [resolve(46,a,104,a)].
% 1.66/1.91  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),C) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)).  [resolve(46,a,105,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).  [resolve(46,a,106,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat).  [resolve(46,a,107,a)].
% 1.66/1.92  108 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom).  [assumption].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A),B,tc_Int_Oint).  [resolve(108,a,47,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),B,tc_Int_Oint).  [resolve(108,a,48,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(108,a,49,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(108,a,50,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint).  [resolve(108,a,51,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint),B).  [resolve(108,a,52,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C)).  [resolve(108,a,53,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),C).  [resolve(108,a,54,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C)).  [resolve(108,a,55,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),C) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint).  [resolve(108,a,57,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint).  [resolve(108,a,58,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(108,a,59,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Int_Oint).  [resolve(108,a,60,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),D)).  [resolve(108,a,63,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_nat)).  [resolve(108,a,64,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint),B).  [resolve(108,a,66,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(108,a,67,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint).  [resolve(108,a,68,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A) = A.  [resolve(108,a,69,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A.  [resolve(108,a,70,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint).  [resolve(108,a,72,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint).  [resolve(108,a,73,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)).  [resolve(108,a,74,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A).  [resolve(108,a,76,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint).  [resolve(108,a,78,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint).  [resolve(108,a,80,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint).  [resolve(108,a,81,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint).  [resolve(108,a,82,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C),tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(108,a,83,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,A,tc_Int_Oint).  [resolve(108,a,84,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),A).  [resolve(108,a,86,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),B,tc_Int_Oint) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),B).  [resolve(108,a,87,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),A).  [resolve(108,a,88,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)).  [resolve(108,a,89,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),A) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_Suc,B)).  [resolve(108,a,90,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),D),tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(108,a,91,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(108,a,92,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(108,a,93,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint).  [resolve(108,a,95,a)].
% 1.66/1.92  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint).  [resolve(108,a,96,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A.  [resolve(108,a,97,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A.  [resolve(108,a,98,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(108,a,100,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),C,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),D),C,tc_Int_Oint).  [resolve(108,a,101,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(108,a,102,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_nat)) = A.  [resolve(108,a,103,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),C)).  [resolve(108,a,104,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),C) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)).  [resolve(108,a,105,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(108,a,106,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint).  [resolve(108,a,107,a)].
% 1.66/1.92  109 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom).  [assumption].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex).  [resolve(109,a,47,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),B,tc_Complex_Ocomplex).  [resolve(109,a,48,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex).  [resolve(109,a,49,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(109,a,50,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex).  [resolve(109,a,51,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),B).  [resolve(109,a,52,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)).  [resolve(109,a,53,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C).  [resolve(109,a,54,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C)).  [resolve(109,a,55,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(109,a,57,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(109,a,58,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(109,a,59,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Complex_Ocomplex).  [resolve(109,a,60,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D)).  [resolve(109,a,63,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_nat)).  [resolve(109,a,64,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B).  [resolve(109,a,66,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex).  [resolve(109,a,67,a)].
% 1.66/1.92  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(109,a,68,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = A.  [resolve(109,a,69,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A.  [resolve(109,a,70,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A),tc_Complex_Ocomplex).  [resolve(109,a,72,a)].
% 1.66/1.92  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex).  [resolve(109,a,73,a)].
% 1.66/1.92  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(c_Suc,B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)).  [resolve(109,a,74,a)].
% 1.66/1.92  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A).  [resolve(109,a,76,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex).  [resolve(109,a,78,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex).  [resolve(109,a,80,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(109,a,81,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(109,a,82,a)].
% 1.66/1.93  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(109,a,83,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,A,tc_Complex_Ocomplex).  [resolve(109,a,84,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),A).  [resolve(109,a,86,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),B,tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),B).  [resolve(109,a,87,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),A).  [resolve(109,a,88,a)].
% 1.66/1.93  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(c_Suc,B)).  [resolve(109,a,89,a)].
% 1.66/1.93  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),A) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(c_Suc,B)).  [resolve(109,a,90,a)].
% 1.66/1.93  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),hAPP(c_Power_Opower__class_Opower(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(109,a,91,a)].
% 1.66/1.93  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(109,a,92,a)].
% 1.66/1.93  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(109,a,93,a)].
% 1.66/1.93  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(109,a,95,a)].
% 1.66/1.93  Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex).  [resolve(109,a,96,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A.  [resolve(109,a,97,a)].
% 1.66/1.93  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A.  [resolve(109,a,98,a)].
% 1.66/1.93  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(109,a,100,a)].
% 1.74/2.03  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),D),C,tc_Complex_Ocomplex).  [resolve(109,a,101,a)].
% 1.74/2.03  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(109,a,102,a)].
% 1.74/2.03  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_nat)) = A.  [resolve(109,a,103,a)].
% 1.74/2.03  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C)).  [resolve(109,a,104,a)].
% 1.74/2.03  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)).  [resolve(109,a,105,a)].
% 1.74/2.03  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),hAPP(c_Power_Opower__class_Opower(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(109,a,106,a)].
% 1.74/2.03  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(109,a,107,a)].
% 1.74/2.03  110 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom).  [assumption].
% 1.74/2.03  111 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = hAPP(c_Finite__Set_Osetsum(E,C,A),D) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(D,B,E,C,A),D,C) # label(cls_setsum__cong2_0) # label(axiom).  [assumption].
% 1.74/2.03  112 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),hAPP(c_Suc,D))) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),hAPP(B,D),A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_1) # label(axiom).  [assumption].
% 1.74/2.03  113 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)) = c_HOL_Oplus__class_Oplus(hAPP(B,C),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),tc_nat),D)),A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_setsum__head__upt__Suc_0) # label(axiom).  [assumption].
% 1.74/2.03  114 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom).  [assumption].
% 1.74/2.03  115 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom).  [assumption].
% 1.74/2.03  116 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom).  [assumption].
% 1.74/2.03  117 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom).  [assumption].
% 1.74/2.03  118 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom).  [assumption].
% 1.74/2.03  119 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = hAPP(c_Finite__Set_Osetsum(E,C,A),D) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(D,B,E,C,A),D,C) # label(cls_setsum__cong_0) # label(axiom).  [assumption].
% 1.74/2.03  120 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom).  [assumption].
% 1.74/2.03  121 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom).  [assumption].
% 1.74/2.03  122 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OlessThan(hAPP(c_Suc,C),tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OlessThan(C,tc_nat)),hAPP(B,C),A) # label(cls_setsum__lessThan__Suc_0) # label(axiom).  [assumption].
% 1.74/2.03  123 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom).  [assumption].
% 1.74/2.03  124 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom).  [assumption].
% 1.74/2.03  125 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = c_HOL_Ozero__class_Ozero(A) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(D,B,C,A),D,C) # label(cls_setsum__0_H_0) # label(axiom).  [assumption].
% 1.74/2.03  126 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(C,B,D,E,A)) != hAPP(D,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(C,B,D,E,A)) | hAPP(c_Finite__Set_Osetsum(B,E,A),C) = hAPP(c_Finite__Set_Osetsum(D,E,A),C) # label(cls_setsum__cong2_1) # label(axiom).  [assumption].
% 1.74/2.03  127 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(C,B,D,E,A)) != hAPP(D,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(C,B,D,E,A)) | hAPP(c_Finite__Set_Osetsum(B,E,A),C) = hAPP(c_Finite__Set_Osetsum(D,E,A),C) # label(cls_setsum__cong_1) # label(axiom).  [assumption].
% 1.74/2.03  128 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(c_Finite__Set_Osetsum(C,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) = hAPP(c_Finite__Set_Osetsum(F,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B),A),E)) # label(cls_setsum__ivl__cong_1) # label(axiom).  [assumption].
% 1.74/2.03  129 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(c_Finite__Set_Osetsum(C,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) = hAPP(c_Finite__Set_Osetsum(F,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) | hBOOL(hAPP(c_lessequals(D,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B))) # label(cls_setsum__ivl__cong_0) # label(axiom).  [assumption].
% 1.74/2.03  130 -class_OrderedGroup_Ocomm__monoid__add(A) | c_List_Olistsum(B,A) = hAPP(c_Finite__Set_Osetsum(c_List_Onth(B,A),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osize__class_Osize(B,tc_List_Olist(A)))) # label(cls_listsum__setsum__nth_0) # label(axiom).  [assumption].
% 1.74/2.03  131 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),tc_nat),hAPP(c_Suc,D))) = hAPP(c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom).  [assumption].
% 1.74/2.03  132 -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,tc_nat),E)),A) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_setsum__add__nat__ivl_0) # label(axiom).  [assumption].
% 1.74/2.03  133 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),hAPP(c_Suc,D))) = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_0) # label(axiom).  [assumption].
% 1.74/2.03  134 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),B,A),C) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__0_0) # label(axiom).  [assumption].
% 1.74/2.03  135 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom).  [assumption].
% 1.74/2.03  136 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(C,B,D,A)) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_Finite__Set_Osetsum(B,D,A),C) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__0_H_1) # label(axiom).  [assumption].
% 1.74/2.03  137 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,C) # label(cls_setsum__def_1) # label(axiom).  [assumption].
% 1.74/2.03  138 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,C) # label(cls_setsum__infinite_0) # label(axiom).  [assumption].
% 1.74/2.03  139 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(C,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B)) != hAPP(F,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B)) | hAPP(c_Finite__Set_Osetsum(C,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) = hAPP(c_Finite__Set_Osetsum(F,A,B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),E)) # label(cls_setsum__ivl__cong_2) # label(axiom).  [assumption].
% 1.74/2.03  140 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),C)) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom).  [assumption].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_nat),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(C,A,D,B,tc_nat),C,B).  [resolve(110,a,111,a)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(A,C),tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(110,a,112,a)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = c_HOL_Oplus__class_Oplus(hAPP(A,B),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),C)),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(110,a,113,a)].
% 1.74/2.03  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)).  [resolve(110,a,114,b)].
% 1.74/2.03  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(110,a,115,b)].
% 1.74/2.03  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(110,a,118,b)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_nat),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(C,A,D,B,tc_nat),C,B).  [resolve(110,a,119,a)].
% 1.74/2.03  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(110,a,120,b)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),c_SetInterval_Oord__class_OlessThan(hAPP(c_Suc,B),tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),c_SetInterval_Oord__class_OlessThan(B,tc_nat)),hAPP(A,B),tc_nat).  [resolve(110,a,122,a)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(C,A,B,tc_nat),C,B).  [resolve(110,a,125,a)].
% 1.74/2.03  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_nat)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_nat)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_nat),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_nat),B).  [resolve(110,a,126,a)].
% 1.74/2.03  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_nat)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_nat)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_nat),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_nat),B).  [resolve(110,a,127,a)].
% 1.74/2.03  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat),A),D)).  [resolve(110,a,128,b)].
% 1.74/2.03  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat))).  [resolve(110,a,129,b)].
% 1.74/2.03  Derived: c_List_Olistsum(A,tc_nat) = hAPP(c_Finite__Set_Osetsum(c_List_Onth(A,tc_nat),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osize__class_Osize(A,tc_List_Olist(tc_nat)))).  [resolve(110,a,130,a)].
% 1.74/2.03  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)).  [resolve(110,a,131,a)].
% 1.74/2.03  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),tc_nat) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(110,a,132,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(110,a,133,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),A,tc_nat),B) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(110,a,134,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(110,a,135,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(B,A,C,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Finite__Set_Osetsum(A,C,tc_nat),B) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(110,a,136,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(C,B).  [resolve(110,a,137,a)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat)) | hAPP(c_Finite__Set_Osetsum(B,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)).  [resolve(110,a,139,b)].
% 1.74/2.04  Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(110,a,140,a)].
% 1.74/2.04  141 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom).  [assumption].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_Int_Oint),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(C,A,D,B,tc_Int_Oint),C,B).  [resolve(141,a,111,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(A,C),tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(141,a,112,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = c_HOL_Oplus__class_Oplus(hAPP(A,B),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),C)),tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(141,a,113,a)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)).  [resolve(141,a,114,b)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(141,a,115,b)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(141,a,118,b)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_Int_Oint),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(C,A,D,B,tc_Int_Oint),C,B).  [resolve(141,a,119,a)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(141,a,120,b)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),c_SetInterval_Oord__class_OlessThan(hAPP(c_Suc,B),tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),c_SetInterval_Oord__class_OlessThan(B,tc_nat)),hAPP(A,B),tc_Int_Oint).  [resolve(141,a,122,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(C,A,B,tc_Int_Oint),C,B).  [resolve(141,a,125,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_Int_Oint)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_Int_Oint)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_Int_Oint),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_Int_Oint),B).  [resolve(141,a,126,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_Int_Oint)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_Int_Oint)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_Int_Oint),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_Int_Oint),B).  [resolve(141,a,127,a)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint),A),D)).  [resolve(141,a,128,b)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint))).  [resolve(141,a,129,b)].
% 1.74/2.04  Derived: c_List_Olistsum(A,tc_Int_Oint) = hAPP(c_Finite__Set_Osetsum(c_List_Onth(A,tc_Int_Oint),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osize__class_Osize(A,tc_List_Olist(tc_Int_Oint)))).  [resolve(141,a,130,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Int_Oint,tc_nat),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)).  [resolve(141,a,131,a)].
% 1.74/2.04  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),tc_Int_Oint) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(141,a,132,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(141,a,133,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint,A),A,tc_Int_Oint),B) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(141,a,134,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(141,a,135,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(B,A,C,tc_Int_Oint)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(A,C,tc_Int_Oint),B) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(141,a,136,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Ofinite(C,B).  [resolve(141,a,137,a)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint)) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)).  [resolve(141,a,139,b)].
% 1.74/2.04  Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(141,a,140,a)].
% 1.74/2.04  142 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom).  [assumption].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Complex_Ocomplex),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_Complex_Ocomplex),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(C,A,D,B,tc_Complex_Ocomplex),C,B).  [resolve(142,a,111,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(A,C),tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(142,a,112,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = c_HOL_Oplus__class_Oplus(hAPP(A,B),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),C)),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(142,a,113,a)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),C)).  [resolve(142,a,114,b)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)).  [resolve(142,a,115,b)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)).  [resolve(142,a,118,b)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Complex_Ocomplex),C) = hAPP(c_Finite__Set_Osetsum(D,B,tc_Complex_Ocomplex),C) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(C,A,D,B,tc_Complex_Ocomplex),C,B).  [resolve(142,a,119,a)].
% 1.74/2.04  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)).  [resolve(142,a,120,b)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(hAPP(c_Suc,B),tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(B,tc_nat)),hAPP(A,B),tc_Complex_Ocomplex).  [resolve(142,a,122,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Complex_Ocomplex),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(C,A,B,tc_Complex_Ocomplex),C,B).  [resolve(142,a,125,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_Complex_Ocomplex)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1(B,A,C,D,tc_Complex_Ocomplex)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_Complex_Ocomplex),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_Complex_Ocomplex),B).  [resolve(142,a,126,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_Complex_Ocomplex)) != hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1(B,A,C,D,tc_Complex_Ocomplex)) | hAPP(c_Finite__Set_Osetsum(A,D,tc_Complex_Ocomplex),B) = hAPP(c_Finite__Set_Osetsum(C,D,tc_Complex_Ocomplex),B).  [resolve(142,a,127,a)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex),A),D)).  [resolve(142,a,128,b)].
% 1.74/2.04  Derived: -class_HOL_Oord(A) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex))).  [resolve(142,a,129,b)].
% 1.74/2.04  Derived: c_List_Olistsum(A,tc_Complex_Ocomplex) = hAPP(c_Finite__Set_Osetsum(c_List_Onth(A,tc_Complex_Ocomplex),tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osize__class_Osize(A,tc_List_Olist(tc_Complex_Ocomplex)))).  [resolve(142,a,130,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)).  [resolve(142,a,131,a)].
% 1.74/2.04  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),tc_Complex_Ocomplex) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(142,a,132,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)).  [resolve(142,a,133,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex,A),A,tc_Complex_Ocomplex),B) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(142,a,134,a)].
% 1.74/2.04  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Complex_Ocomplex),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(142,a,135,a)].
% 1.74/2.04  Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(B,A,C,tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_Finite__Set_Osetsum(A,C,tc_Complex_Ocomplex),B) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(142,a,136,a)].
% 1.88/2.12  Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Complex_Ocomplex),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Finite__Set_Ofinite(C,B).  [resolve(142,a,137,a)].
% 1.88/2.12  Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex)) | hAPP(c_Finite__Set_Osetsum(B,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)) = hAPP(c_Finite__Set_Osetsum(E,A,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D)).  [resolve(142,a,139,b)].
% 1.88/2.12  Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(142,a,140,a)].
% 1.88/2.12  143 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom).  [assumption].
% 1.88/2.12  144 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom).  [assumption].
% 1.88/2.12  145 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom).  [assumption].
% 1.88/2.12  146 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom).  [assumption].
% 1.88/2.12  147 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom).  [assumption].
% 1.88/2.12  148 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom).  [assumption].
% 1.88/2.12  149 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__less__mult__pos_0) # label(axiom).  [assumption].
% 1.88/2.12  150 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom).  [assumption].
% 1.88/2.12  151 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom).  [assumption].
% 1.88/2.12  152 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom).  [assumption].
% 1.88/2.12  153 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom).  [assumption].
% 1.88/2.12  154 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom).  [assumption].
% 1.88/2.12  155 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom).  [assumption].
% 1.88/2.12  156 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom).  [assumption].
% 1.88/2.12  157 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom).  [assumption].
% 1.88/2.12  158 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom).  [assumption].
% 1.88/2.12  159 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom).  [assumption].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(143,a,144,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(143,a,145,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(143,a,147,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))).  [resolve(143,a,148,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A))).  [resolve(143,a,149,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(143,a,150,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C))).  [resolve(143,a,151,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))).  [resolve(143,a,152,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(143,a,153,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C))).  [resolve(143,a,154,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))).  [resolve(143,a,155,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(143,a,156,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(143,a,157,a)].
% 1.88/2.12  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(143,a,158,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(143,a,159,a)].
% 1.88/2.13  160 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom).  [assumption].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(160,a,144,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(160,a,145,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(160,a,147,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))).  [resolve(160,a,148,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A))).  [resolve(160,a,149,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(160,a,150,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C))).  [resolve(160,a,151,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))).  [resolve(160,a,152,a)].
% 1.88/2.13  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(160,a,153,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C))).  [resolve(160,a,154,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))).  [resolve(160,a,155,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(160,a,156,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)).  [resolve(160,a,157,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(160,a,158,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(160,a,159,a)].
% 1.90/2.21  161 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom).  [assumption].
% 1.90/2.21  162 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_3) # label(axiom).  [assumption].
% 1.90/2.21  163 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_2) # label(axiom).  [assumption].
% 1.90/2.21  164 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_1) # label(axiom).  [assumption].
% 1.90/2.21  165 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_0) # label(axiom).  [assumption].
% 1.90/2.21  166 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom).  [assumption].
% 1.90/2.21  167 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom).  [assumption].
% 1.90/2.21  168 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B))) # label(cls_zero__le__square_0) # label(axiom).  [assumption].
% 1.90/2.21  169 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__mult__iff_4) # label(axiom).  [assumption].
% 1.90/2.21  170 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__mult__iff_5) # label(axiom).  [assumption].
% 1.90/2.21  171 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_2) # label(axiom).  [assumption].
% 1.90/2.21  172 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom).  [assumption].
% 1.90/2.21  173 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__neg_0) # label(axiom).  [assumption].
% 1.90/2.21  174 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A))) # label(cls_sum__squares__ge__zero_0) # label(axiom).  [assumption].
% 1.90/2.21  175 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__le__mult__iff_0) # label(axiom).  [assumption].
% 1.90/2.21  176 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__le__mult__iff_1) # label(axiom).  [assumption].
% 1.90/2.21  177 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) # label(cls_zero__le__mult__iff_2) # label(axiom).  [assumption].
% 1.90/2.21  178 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B))) # label(cls_zero__le__mult__iff_3) # label(axiom).  [assumption].
% 1.90/2.21  179 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),A))) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom).  [assumption].
% 1.90/2.21  180 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__left__disj_0) # label(axiom).  [assumption].
% 1.90/2.21  181 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__left__disj_3) # label(axiom).  [assumption].
% 1.90/2.21  182 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__right__disj_0) # label(axiom).  [assumption].
% 1.90/2.21  183 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__right__disj_3) # label(axiom).  [assumption].
% 1.90/2.21  184 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__square__less__zero_0) # label(axiom).  [assumption].
% 1.90/2.21  185 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__0__iff_4) # label(axiom).  [assumption].
% 1.90/2.21  186 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_5) # label(axiom).  [assumption].
% 1.90/2.21  187 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__cancel__left__pos_1) # label(axiom).  [assumption].
% 1.90/2.21  188 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__le__cancel__left__pos_0) # label(axiom).  [assumption].
% 1.90/2.21  189 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_1) # label(axiom).  [assumption].
% 1.90/2.21  190 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_0) # label(axiom).  [assumption].
% 1.90/2.21  191 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),B),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom).  [assumption].
% 1.90/2.21  192 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom).  [assumption].
% 1.90/2.21  193 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom).  [assumption].
% 1.90/2.21  194 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),C),A))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom).  [assumption].
% 1.90/2.21  195 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__right__disj_5) # label(axiom).  [assumption].
% 1.90/2.21  196 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__less__cancel__right__disj_4) # label(axiom).  [assumption].
% 1.90/2.21  197 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_mult__strict__right__mono__neg_0) # label(axiom).  [assumption].
% 1.90/2.21  198 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__disj_5) # label(axiom).  [assumption].
% 1.90/2.21  199 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__disj_4) # label(axiom).  [assumption].
% 1.90/2.21  200 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_mult__strict__left__mono__neg_0) # label(axiom).  [assumption].
% 1.90/2.21  201 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__pos_1) # label(axiom).  [assumption].
% 1.90/2.21  202 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__less__cancel__left__pos_0) # label(axiom).  [assumption].
% 1.90/2.21  203 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_1) # label(axiom).  [assumption].
% 1.90/2.21  204 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_0) # label(axiom).  [assumption].
% 1.90/2.21  205 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom).  [assumption].
% 1.90/2.21  206 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A)),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom).  [assumption].
% 1.90/2.21  207 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__left__disj_1) # label(axiom).  [assumption].
% 1.90/2.21  208 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__left__disj_2) # label(axiom).  [assumption].
% 1.90/2.21  209 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) # label(cls_mult__less__cancel__right__disj_1) # label(axiom).  [assumption].
% 1.90/2.21  210 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),B))) # label(cls_mult__less__cancel__right__disj_2) # label(axiom).  [assumption].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,162,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,163,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,164,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,165,a)].
% 1.90/2.21  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(161,a,166,a)].
% 1.90/2.21  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(161,a,167,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A))).  [resolve(161,a,168,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(161,a,169,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,170,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,171,a)].
% 1.90/2.21  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,172,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,173,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint))).  [resolve(161,a,174,a)].
% 1.90/2.21  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))).  [resolve(161,a,175,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A))).  [resolve(161,a,176,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B))).  [resolve(161,a,177,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A))).  [resolve(161,a,178,a)].
% 1.90/2.22  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint))).  [resolve(161,a,179,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))).  [resolve(161,a,180,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))).  [resolve(161,a,181,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))).  [resolve(161,a,182,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))).  [resolve(161,a,183,a)].
% 1.90/2.22  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,184,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(161,a,185,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,186,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(161,a,187,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,189,a)].
% 1.90/2.22  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,190,a)].
% 1.90/2.22  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,191,a)].
% 1.90/2.22  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,192,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint))) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(161,a,193,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),B),tc_Int_Oint))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(161,a,194,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,195,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,198,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)).  [resolve(161,a,202,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(161,a,204,a)].
% 2.06/2.37  Derived: -class_OrderedGroup_Omonoid__mult(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(161,a,205,a)].
% 2.06/2.37  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(161,a,206,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))).  [resolve(161,a,207,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))).  [resolve(161,a,208,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))).  [resolve(161,a,209,a)].
% 2.06/2.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A))).  [resolve(161,a,210,a)].
% 2.06/2.37  211 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom).  [assumption].
% 2.06/2.37  212 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_3) # label(axiom).  [assumption].
% 2.06/2.37  213 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_3) # label(axiom).  [assumption].
% 2.06/2.37  214 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) # label(cls_mult__frac__frac_0) # label(axiom).  [assumption].
% 2.06/2.37  215 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(C,B,A) # label(cls_inverse__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  216 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  217 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),B,A) # label(cls_eq__divide__imp_0) # label(axiom).  [assumption].
% 2.06/2.37  218 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom).  [assumption].
% 2.06/2.37  219 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom).  [assumption].
% 2.06/2.37  220 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom).  [assumption].
% 2.06/2.37  221 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) != c_Int_Onumber__class_Onumber__of(C,A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_1) # label(axiom).  [assumption].
% 2.06/2.37  222 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_2) # label(axiom).  [assumption].
% 2.06/2.37  223 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_4) # label(axiom).  [assumption].
% 2.06/2.37  224 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_diff__divide__distrib_0) # label(axiom).  [assumption].
% 2.06/2.37  225 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_1) # label(axiom).  [assumption].
% 2.06/2.37  226 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq__number__of_2) # label(axiom).  [assumption].
% 2.06/2.37  227 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_2) # label(axiom).  [assumption].
% 2.06/2.37  228 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,D,A) | hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),D) = C | D = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_0) # label(axiom).  [assumption].
% 2.06/2.37  229 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  230 -class_Ring__and__Field_Ofield(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),E),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  231 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom).  [assumption].
% 2.06/2.37  232 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),C,A) # label(cls_eq__divide__eq__number__of_4) # label(axiom).  [assumption].
% 2.06/2.37  233 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__add_0) # label(axiom).  [assumption].
% 2.06/2.37  234 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom).  [assumption].
% 2.06/2.37  235 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(C,hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom).  [assumption].
% 2.06/2.37  236 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_divide__1_0) # label(axiom).  [assumption].
% 2.06/2.37  237 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__eq__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  238 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  239 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),hAPP(c_Power_Opower__class_Opower(B,A),C),A) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A),C) # label(cls_power__one__over_0) # label(axiom).  [assumption].
% 2.06/2.37  240 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_inverse__mult__distrib_0) # label(axiom).  [assumption].
% 2.06/2.37  241 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),C,A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_4) # label(axiom).  [assumption].
% 2.06/2.37  242 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom).  [assumption].
% 2.06/2.37  243 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom).  [assumption].
% 2.06/2.37  244 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom).  [assumption].
% 2.06/2.37  245 -class_Ring__and__Field_Ofield(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ominus__class_Ominus(C,D,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(B,A),C),hAPP(c_Power_Opower__class_Opower(B,A),D),A) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom).  [assumption].
% 2.06/2.37  246 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_3) # label(axiom).  [assumption].
% 2.06/2.37  247 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),A),c_Int_Onumber__class_Onumber__of(C,A)) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_0) # label(axiom).  [assumption].
% 2.06/2.37  248 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),A),c_Int_Onumber__class_Onumber__of(C,A)) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_0) # label(axiom).  [assumption].
% 2.06/2.37  249 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B),B,A) # label(cls_eq__divide__eq_4) # label(axiom).  [assumption].
% 2.06/2.37  250 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),C,A) = c_Int_Onumber__class_Onumber__of(B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_3) # label(axiom).  [assumption].
% 2.06/2.37  251 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom).  [assumption].
% 2.06/2.37  252 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom).  [assumption].
% 2.06/2.37  253 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom).  [assumption].
% 2.06/2.37  254 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),D) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),C,A) # label(cls_mult__frac__num_0) # label(axiom).  [assumption].
% 2.06/2.37  255 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_add__divide__distrib_0) # label(axiom).  [assumption].
% 2.06/2.37  256 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom).  [assumption].
% 2.06/2.37  257 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),E),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  258 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  259 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),A),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  260 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom).  [assumption].
% 2.06/2.37  261 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_4) # label(axiom).  [assumption].
% 2.06/2.37  262 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_1) # label(axiom).  [assumption].
% 2.06/2.37  263 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_Int_Onumber__class_Onumber__of(D,A) | B = hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),A),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_0) # label(axiom).  [assumption].
% 2.06/2.37  264 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_divide__inverse_0) # label(axiom).  [assumption].
% 2.06/2.37  265 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom).  [assumption].
% 2.06/2.37  266 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom).  [assumption].
% 2.06/2.37  267 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom).  [assumption].
% 2.06/2.37  268 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom).  [assumption].
% 2.06/2.37  269 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom).  [assumption].
% 2.06/2.37  270 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_Int_Onumber__class_Onumber__of(B,A)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_inverse__eq__divide__number__of_0) # label(axiom).  [assumption].
% 2.06/2.37  271 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),E) = hAPP(c_HOL_Otimes__class_Otimes(D,A),C) # label(cls_frac__eq__eq_0) # label(axiom).  [assumption].
% 2.06/2.37  272 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != hAPP(c_HOL_Otimes__class_Otimes(D,A),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom).  [assumption].
% 2.06/2.37  273 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom).  [assumption].
% 2.06/2.37  274 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),A),D) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(B,A),D),hAPP(c_Power_Opower__class_Opower(C,A),D),A) # label(cls_power__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  275 -class_Ring__and__Field_Ofield(A) | hAPP(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(B,A),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(B,A),C),c_HOL_Oone__class_Oone(A),A),c_HOL_Ominus__class_Ominus(B,c_HOL_Oone__class_Oone(A),A),A) | B = c_HOL_Oone__class_Oone(A) # label(cls_geometric__sum_0) # label(axiom).  [assumption].
% 2.06/2.37  276 -class_Ring__and__Field_Ofield(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),A),D) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(B,A),D),hAPP(c_Power_Opower__class_Opower(C,A),D),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom).  [assumption].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,212,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,213,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex).  [resolve(211,a,214,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(B,A,tc_Complex_Ocomplex).  [resolve(211,a,215,a)].
% 2.06/2.37  Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B.  [resolve(211,a,216,a)].
% 2.06/2.37  Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex).  [resolve(211,a,217,a)].
% 2.06/2.37  Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex) = B.  [resolve(211,a,218,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,221,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex).  [resolve(211,a,222,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,223,a)].
% 2.06/2.37  Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,224,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,225,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,226,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,227,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = B | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,228,a)].
% 2.06/2.37  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,229,a)].
% 2.06/2.37  Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),D),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,230,a)].
% 2.06/2.37  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,231,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),B,tc_Complex_Ocomplex).  [resolve(211,a,232,a)].
% 2.06/2.37  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,233,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,234,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,235,a)].
% 2.06/2.37  Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A.  [resolve(211,a,236,a)].
% 2.06/2.37  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex).  [resolve(211,a,237,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B).  [resolve(211,a,239,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)).  [resolve(211,a,240,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),B,tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex).  [resolve(211,a,241,a)].
% 2.06/2.37  Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(211,a,242,a)].
% 2.06/2.37  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,C,tc_nat)) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,245,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,247,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,248,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex).  [resolve(211,a,249,a)].
% 2.06/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(211,a,251,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,252,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,253,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),B,tc_Complex_Ocomplex).  [resolve(211,a,254,a)].
% 2.14/2.37  Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,255,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(211,a,256,a)].
% 2.14/2.37  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),D),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,257,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,258,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,259,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(211,a,260,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,261,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,262,a)].
% 2.14/2.37  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex) | A = hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,263,a)].
% 2.19/2.47  Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)).  [resolve(211,a,264,a)].
% 2.19/2.47  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,266,a)].
% 2.19/2.47  Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,267,a)].
% 2.19/2.47  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,268,a)].
% 2.19/2.47  Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),D) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B).  [resolve(211,a,271,a)].
% 2.19/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) != hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,D,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(C,B,tc_Complex_Ocomplex).  [resolve(211,a,272,a)].
% 2.19/2.47  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,273,a)].
% 2.19/2.47  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(211,a,274,a)].
% 2.19/2.47  Derived: hAPP(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(211,a,275,a)].
% 2.19/2.47  Derived: hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(211,a,276,a)].
% 2.19/2.47  277 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom).  [assumption].
% 2.19/2.47  278 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__eq__mult_3) # label(axiom).  [assumption].
% 2.28/2.52  279 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__eq__mult_2) # label(axiom).  [assumption].
% 2.28/2.52  280 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__eq__mult_1) # label(axiom).  [assumption].
% 2.28/2.52  281 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__eq__mult_0) # label(axiom).  [assumption].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(277,a,278,a)].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(277,a,279,a)].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(277,a,280,a)].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(277,a,281,a)].
% 2.28/2.52  282 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom).  [assumption].
% 2.28/2.52  283 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__mult_0) # label(axiom).  [assumption].
% 2.28/2.52  284 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom).  [assumption].
% 2.28/2.52  285 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_0) # label(axiom).  [assumption].
% 2.28/2.52  286 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),D))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__even_0) # label(axiom).  [assumption].
% 2.28/2.52  287 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom).  [assumption].
% 2.28/2.52  288 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  289 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom).  [assumption].
% 2.28/2.52  290 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_2) # label(axiom).  [assumption].
% 2.28/2.52  291 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__le__power__eq__number__of_0) # label(axiom).  [assumption].
% 2.28/2.52  292 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom).  [assumption].
% 2.28/2.52  293 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)) = c_Nat_Osemiring__1__class_Oof__nat(B,A) # label(cls_abs__of__nat_0) # label(axiom).  [assumption].
% 2.28/2.52  294 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__left__le__one__le_0) # label(axiom).  [assumption].
% 2.28/2.52  295 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__right__le__one__le_0) # label(axiom).  [assumption].
% 2.28/2.52  296 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),C),A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),D)) # label(cls_abs__mult__less_0) # label(axiom).  [assumption].
% 2.28/2.52  297 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__less__zero__eq__number__of_2) # label(axiom).  [assumption].
% 2.28/2.52  298 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_1) # label(axiom).  [assumption].
% 2.28/2.52  299 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_1) # label(axiom).  [assumption].
% 2.28/2.52  300 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C)) # label(cls_abs__less__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  301 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),B) # label(cls_abs__mult__self_0) # label(axiom).  [assumption].
% 2.28/2.52  302 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C) = hAPP(c_Power_Opower__class_Opower(B,A),C) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__even__abs_0) # label(axiom).  [assumption].
% 2.28/2.52  303 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_2) # label(axiom).  [assumption].
% 2.28/2.52  304 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(D,B,A)),A),C)) # label(cls_abs__diff__less__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  305 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(C,D,A),A),B)) # label(cls_abs__diff__less__iff_2) # label(axiom).  [assumption].
% 2.28/2.52  306 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_abs__mult__pos_0) # label(axiom).  [assumption].
% 2.28/2.52  307 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__dvd__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  308 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_abs__dvd__iff_1) # label(axiom).  [assumption].
% 2.28/2.52  309 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Oabs__class_Oabs(A),C),A) # label(cls_dvd__abs__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  310 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Oabs__class_Oabs(A),C),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__abs__iff_1) # label(axiom).  [assumption].
% 2.28/2.52  311 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Int_Onumber__class_Onumber__of(B,A)) = c_Int_Onumber__class_Onumber__of(B,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__number__of_1) # label(axiom).  [assumption].
% 2.28/2.52  312 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_5) # label(axiom).  [assumption].
% 2.28/2.52  313 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) # label(cls_zero__le__power__eq_0) # label(axiom).  [assumption].
% 2.28/2.52  314 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom).  [assumption].
% 2.28/2.52  315 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom).  [assumption].
% 2.28/2.52  316 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom).  [assumption].
% 2.28/2.52  317 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(C,A),B))) # label(cls_zero__le__power__iff_0) # label(axiom).  [assumption].
% 2.28/2.52  318 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_2) # label(axiom).  [assumption].
% 2.28/2.52  319 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C))) # label(cls_zero__le__power__abs_0) # label(axiom).  [assumption].
% 2.28/2.52  320 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_4) # label(axiom).  [assumption].
% 2.28/2.52  321 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_3) # label(axiom).  [assumption].
% 2.28/2.52  322 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom).  [assumption].
% 2.28/2.52  323 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_1) # label(axiom).  [assumption].
% 2.28/2.52  324 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom).  [assumption].
% 2.28/2.52  325 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_0) # label(axiom).  [assumption].
% 2.28/2.52  326 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_1) # label(axiom).  [assumption].
% 2.28/2.52  327 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__iff_2) # label(axiom).  [assumption].
% 2.28/2.52  328 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_1) # label(axiom).  [assumption].
% 2.28/2.52  329 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_1) # label(axiom).  [assumption].
% 2.28/2.52  330 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__less__power__eq__number__of_0) # label(axiom).  [assumption].
% 2.28/2.52  331 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq__number__of_4) # label(axiom).  [assumption].
% 2.28/2.52  332 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_5) # label(axiom).  [assumption].
% 2.28/2.52  333 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)),A),D)) # label(cls_abs__diff__less__iff_1) # label(axiom).  [assumption].
% 2.28/2.52  334 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_4) # label(axiom).  [assumption].
% 2.28/2.52  335 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),c_Int_Onumber__class_Onumber__of(C,tc_nat)) = hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__even__abs__number__of_0) # label(axiom).  [assumption].
% 2.28/2.52  336 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) != hAPP(c_HOL_Oabs__class_Oabs(A),C) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__if__abs__eq_0) # label(axiom).  [assumption].
% 2.28/2.52  337 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C) # label(cls_power__abs_0) # label(axiom).  [assumption].
% 2.28/2.52  338 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq__number__of_2) # label(axiom).  [assumption].
% 2.28/2.52  339 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom).  [assumption].
% 2.28/2.52  340 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) # label(cls_zero__less__power__eq__number__of_3) # label(axiom).  [assumption].
% 2.28/2.52  341 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq_4) # label(axiom).  [assumption].
% 2.28/2.52  342 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) # label(cls_zero__less__power__eq_0) # label(axiom).  [assumption].
% 2.28/2.52  343 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_0) # label(axiom).  [assumption].
% 2.28/2.52  344 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_5) # label(axiom).  [assumption].
% 2.28/2.52  345 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power__iff_1) # label(axiom).  [assumption].
% 2.28/2.52  346 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_1) # label(axiom).  [assumption].
% 2.28/2.52  347 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_3) # label(axiom).  [assumption].
% 2.28/2.52  348 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_0) # label(axiom).  [assumption].
% 2.28/2.52  349 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)))) # label(cls_zero__less__power__eq_3) # label(axiom).  [assumption].
% 2.28/2.52  350 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq_2) # label(axiom).  [assumption].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)).  [resolve(282,a,283,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,284,a)].
% 2.28/2.52  Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,285,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),C))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,286,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | B = A.  [resolve(282,a,287,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,288,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,289,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)))).  [resolve(282,a,291,a)].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) = c_HOL_Oone__class_Oone(tc_Int_Oint).  [resolve(282,a,292,a)].
% 2.28/2.52  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)) = c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint).  [resolve(282,a,293,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(282,a,294,a)].
% 2.28/2.52  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(282,a,295,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),C)).  [resolve(282,a,296,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat).  [resolve(282,a,297,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat).  [resolve(282,a,298,a)].
% 2.28/2.53  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,299,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B)).  [resolve(282,a,300,a)].
% 2.28/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),A).  [resolve(282,a,301,a)].
% 2.28/2.53  Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,302,a)].
% 2.28/2.53  Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,303,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint)),tc_Int_Oint),B)).  [resolve(282,a,304,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint),A)).  [resolve(282,a,305,a)].
% 2.28/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)).  [resolve(282,a,306,a)].
% 2.28/2.53  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint).  [resolve(282,a,307,a)].
% 2.28/2.53  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(282,a,308,a)].
% 2.28/2.53  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint).  [resolve(282,a,309,a)].
% 2.28/2.53  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(282,a,310,a)].
% 2.28/2.53  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,311,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))).  [resolve(282,a,313,a)].
% 2.28/2.53  Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,318,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B))).  [resolve(282,a,319,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,320,a)].
% 2.28/2.53  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,321,a)].
% 2.28/2.53  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,323,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,324,a)].
% 2.28/2.53  Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,325,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).  [resolve(282,a,326,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,328,a)].
% 2.28/2.53  Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat).  [resolve(282,a,329,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)))).  [resolve(282,a,330,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(282,a,331,a)].
% 2.28/2.53  Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,332,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),tc_Int_Oint),C)).  [resolve(282,a,333,a)].
% 2.28/2.53  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) != hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B) | c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(282,a,336,a)].
% 2.28/2.53  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B).  [resolve(282,a,337,a)].
% 2.28/2.53  Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,338,a)].
% 2.28/2.53  Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A))) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).  [resolve(282,a,339,a)].
% 2.28/2.53  Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)))).  [resolve(282,a,340,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(282,a,341,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))).  [resolve(282,a,342,a)].
% 2.28/2.53  Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,343,a)].
% 2.28/2.53  Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,344,a)].
% 2.28/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,346,a)].
% 2.36/2.62  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,347,a)].
% 2.36/2.62  Derived: -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,348,a)].
% 2.36/2.62  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)))).  [resolve(282,a,349,a)].
% 2.36/2.62  Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(282,a,350,a)].
% 2.36/2.63  351 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom).  [assumption].
% 2.36/2.63  352 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom).  [assumption].
% 2.36/2.63  353 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom).  [assumption].
% 2.36/2.63  354 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom).  [assumption].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(351,a,352,a)].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(351,a,353,a)].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(351,a,354,a)].
% 2.36/2.63  355 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom).  [assumption].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(355,a,352,a)].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)).  [resolve(355,a,353,a)].
% 2.36/2.63  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(355,a,354,a)].
% 2.36/2.63  356 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom).  [assumption].
% 2.36/2.63  357 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Otimes__class_Otimes(C,A),c_HOL_Ozero__class_Ozero(A)),A) # label(cls_dvd__mult__cancel__right_1) # label(axiom).  [assumption].
% 2.36/2.63  358 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),C),A) # label(cls_dvd__mult__cancel__left_1) # label(axiom).  [assumption].
% 2.36/2.63  359 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) != c_HOL_Oplus__class_Oplus(B,hAPP(c_HOL_Otimes__class_Otimes(C,A),E),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom).  [assumption].
% 2.36/2.63  360 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom).  [assumption].
% 2.36/2.63  361 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom).  [assumption].
% 2.36/2.63  362 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom).  [assumption].
% 2.36/2.63  363 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) # label(cls_dvd__mult__cancel__left_2) # label(axiom).  [assumption].
% 2.36/2.63  364 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult__cancel__right_2) # label(axiom).  [assumption].
% 2.36/2.63  365 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),E),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom).  [assumption].
% 2.36/2.63  366 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),E),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom).  [assumption].
% 2.36/2.63  367 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_dvd__mult__cancel__right_0) # label(axiom).  [assumption].
% 2.36/2.63  368 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) # label(cls_dvd__mult__cancel__left_0) # label(axiom).  [assumption].
% 2.36/2.63  369 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom).  [assumption].
% 2.36/2.63  370 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom).  [assumption].
% 2.36/2.63  371 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom).  [assumption].
% 2.36/2.63  372 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom).  [assumption].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint).  [resolve(356,a,357,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B),tc_Int_Oint).  [resolve(356,a,358,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),D),tc_Int_Oint) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(356,a,359,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C.  [resolve(356,a,360,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint).  [resolve(356,a,363,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint).  [resolve(356,a,364,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),D),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint) | B = D | A = C.  [resolve(356,a,365,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),tc_Int_Oint).  [resolve(356,a,367,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),tc_Int_Oint).  [resolve(356,a,368,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(356,a,369,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(356,a,370,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B.  [resolve(356,a,371,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint).  [resolve(356,a,372,a)].
% 2.36/2.63  373 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom).  [assumption].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_Complex_Ocomplex).  [resolve(373,a,357,a)].
% 2.36/2.63  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),tc_Complex_Ocomplex).  [resolve(373,a,358,a)].
% 2.36/2.63  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(373,a,359,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C.  [resolve(373,a,360,a)].
% 2.48/2.72  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Complex_Ocomplex).  [resolve(373,a,363,a)].
% 2.48/2.72  Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex).  [resolve(373,a,364,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),D),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | B = D | A = C.  [resolve(373,a,365,a)].
% 2.48/2.72  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(373,a,367,a)].
% 2.48/2.72  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex).  [resolve(373,a,368,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(373,a,369,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(373,a,370,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B.  [resolve(373,a,371,a)].
% 2.48/2.72  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(373,a,372,a)].
% 2.48/2.72  374 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom).  [assumption].
% 2.48/2.72  375 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom).  [assumption].
% 2.48/2.72  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(374,a,375,a)].
% 2.48/2.72  376 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom).  [assumption].
% 2.48/2.72  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)).  [resolve(376,a,375,a)].
% 2.48/2.72  377 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom).  [assumption].
% 2.50/2.77  378 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom).  [assumption].
% 2.50/2.77  379 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom).  [assumption].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(377,a,379,a)].
% 2.50/2.77  380 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom).  [assumption].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(380,a,379,a)].
% 2.50/2.77  381 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom).  [assumption].
% 2.50/2.77  382 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom).  [assumption].
% 2.50/2.77  383 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom).  [assumption].
% 2.50/2.77  384 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom).  [assumption].
% 2.50/2.77  385 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom).  [assumption].
% 2.50/2.77  386 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom).  [assumption].
% 2.50/2.77  387 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A))) | -hBOOL(hAPP(c_lessequals(D,A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),A),C),F,A))) # label(cls_le__add__iff2_1) # label(axiom).  [assumption].
% 2.50/2.77  388 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),A),E),F,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,A),E),B,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,A),E),F,A))) # label(cls_le__add__iff2_0) # label(axiom).  [assumption].
% 2.50/2.77  389 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),A),C),D,A),A),F)) # label(cls_le__add__iff1_1) # label(axiom).  [assumption].
% 2.50/2.77  390 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),A),D),E,A),A),F)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),E,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),F,A))) # label(cls_le__add__iff1_0) # label(axiom).  [assumption].
% 2.50/2.77  391 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),A),D),E,A),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),E,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),F,A))) # label(cls_less__add__iff1_0) # label(axiom).  [assumption].
% 2.50/2.77  392 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),A),C),D,A),A),F)) # label(cls_less__add__iff1_1) # label(axiom).  [assumption].
% 2.50/2.77  393 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),A),E),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,A),E),B,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,A),E),F,A))) # label(cls_less__add__iff2_0) # label(axiom).  [assumption].
% 2.50/2.77  394 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),A),C),F,A))) # label(cls_less__add__iff2_1) # label(axiom).  [assumption].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)).  [resolve(381,a,382,a)].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),A)).  [resolve(381,a,383,a)].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),tc_Int_Oint),B),E,tc_Int_Oint))).  [resolve(381,a,387,a)].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint),D),E,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D),A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),D),E,tc_Int_Oint))).  [resolve(381,a,388,a)].
% 2.50/2.77  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),E)).  [resolve(381,a,389,a)].
% 2.50/2.82  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),C),D,tc_Int_Oint),tc_Int_Oint),E)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),D,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),E,tc_Int_Oint))).  [resolve(381,a,390,a)].
% 2.50/2.82  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),C),D,tc_Int_Oint),tc_Int_Oint),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),C),D,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),C),E,tc_Int_Oint))).  [resolve(381,a,391,a)].
% 2.50/2.82  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),E)).  [resolve(381,a,392,a)].
% 2.50/2.82  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint),D),E,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D),A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),D),E,tc_Int_Oint))).  [resolve(381,a,393,a)].
% 2.50/2.82  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),tc_Int_Oint),B),E,tc_Int_Oint))).  [resolve(381,a,394,a)].
% 2.50/2.82  395 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom).  [assumption].
% 2.50/2.82  396 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Oone__class_Oone(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = C # label(cls_inverse__unique_0) # label(axiom).  [assumption].
% 2.50/2.82  397 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != hAPP(c_HOL_Oinverse__class_Oinverse(A),C) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom).  [assumption].
% 2.50/2.82  398 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom).  [assumption].
% 2.50/2.82  399 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom).  [assumption].
% 2.50/2.82  400 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),c_HOL_Oplus__class_Oplus(B,C,A)),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__add_0) # label(axiom).  [assumption].
% 2.50/2.82  401 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B # label(cls_inverse__inverse__eq_0) # label(axiom).  [assumption].
% 2.50/2.82  402 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom).  [assumption].
% 2.50/2.82  403 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom).  [assumption].
% 2.50/2.82  404 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom).  [assumption].
% 2.50/2.82  405 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom).  [assumption].
% 2.50/2.82  406 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom).  [assumption].
% 2.50/2.82  407 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom).  [assumption].
% 2.50/2.82  408 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != hAPP(c_HOL_Oinverse__class_Oinverse(A),C) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom).  [assumption].
% 2.50/2.82  409 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),c_HOL_Ominus__class_Ominus(C,B,A)),A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__diff_0) # label(axiom).  [assumption].
% 2.50/2.82  410 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),C) # label(cls_power__inverse_0) # label(axiom).  [assumption].
% 2.50/2.82  411 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom).  [assumption].
% 2.50/2.82  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = B.  [resolve(395,a,396,a)].
% 2.50/2.82  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B) | A = B.  [resolve(395,a,397,a)].
% 2.50/2.82  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,399,a)].
% 2.50/2.82  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,400,a)].
% 2.60/2.86  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A.  [resolve(395,a,401,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,402,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,403,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(395,a,405,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,406,a)].
% 2.60/2.86  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,407,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B) | A = B | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,408,a)].
% 2.60/2.86  Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,A,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,409,a)].
% 2.60/2.86  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B).  [resolve(395,a,410,a)].
% 2.60/2.86  Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(395,a,411,a)].
% 2.60/2.86  412 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom).  [assumption].
% 2.60/2.86  413 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom).  [assumption].
% 2.60/2.86  414 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom).  [assumption].
% 2.60/2.86  415 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom).  [assumption].
% 2.60/2.86  416 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),A) = hAPP(c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom).  [assumption].
% 2.60/2.86  417 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom).  [assumption].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat).  [resolve(412,a,413,a)].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat).  [resolve(412,a,414,a)].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat).  [resolve(412,a,415,a)].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)).  [resolve(412,a,416,a)].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(412,a,417,a)].
% 2.60/2.86  418 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom).  [assumption].
% 2.60/2.86  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint).  [resolve(418,a,413,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint).  [resolve(418,a,414,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint).  [resolve(418,a,415,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_Int_Oint) = hAPP(c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)).  [resolve(418,a,416,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(418,a,417,a)].
% 2.60/2.87  419 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom).  [assumption].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(419,a,413,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(419,a,414,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(419,a,415,a)].
% 2.60/2.87  Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)).  [resolve(419,a,416,a)].
% 2.66/2.91  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(419,a,417,a)].
% 2.66/2.91  420 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom).  [assumption].
% 2.66/2.91  421 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom).  [assumption].
% 2.66/2.91  422 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom).  [assumption].
% 2.66/2.91  423 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom).  [assumption].
% 2.66/2.91  424 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom).  [assumption].
% 2.66/2.91  425 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom).  [assumption].
% 2.66/2.91  426 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom).  [assumption].
% 2.66/2.91  427 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom).  [assumption].
% 2.66/2.91  428 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom).  [assumption].
% 2.66/2.91  429 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,E,A))) # label(cls_le__add__right__mono_0) # label(axiom).  [assumption].
% 2.66/2.91  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)).  [resolve(420,a,421,a)].
% 2.66/2.91  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)).  [resolve(420,a,422,a)].
% 2.66/2.91  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)).  [resolve(420,a,423,a)].
% 2.66/2.91  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)).  [resolve(420,a,424,a)].
% 2.66/2.91  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)).  [resolve(420,a,425,a)].
% 2.66/2.91  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(420,a,426,a)].
% 2.72/2.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)).  [resolve(420,a,427,a)].
% 2.72/2.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(420,a,428,a)].
% 2.72/2.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint))).  [resolve(420,a,429,a)].
% 2.72/2.96  430 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom).  [assumption].
% 2.72/2.96  431 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A),F,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,F,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,E,A) # label(cls_inf__period_I4_J_0) # label(axiom).  [assumption].
% 2.72/2.96  432 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,hAPP(c_HOL_Otimes__class_Otimes(E,A),F),A),D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,F,A) # label(cls_inf__period_I4_J_1) # label(axiom).  [assumption].
% 2.72/2.96  433 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_dvdI_0) # label(axiom).  [assumption].
% 2.72/2.96  Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat),E,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_nat).  [resolve(430,a,431,a)].
% 2.72/2.96  Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(D,tc_nat),E),tc_nat),C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_nat).  [resolve(430,a,432,a)].
% 2.72/2.96  434 class_Ring__and__Field_Odvd(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Odvd) # label(axiom).  [assumption].
% 2.72/2.96  Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D),tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Int_Oint).  [resolve(434,a,431,a)].
% 2.72/2.96  Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),E),tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Int_Oint).  [resolve(434,a,432,a)].
% 2.72/2.96  435 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom).  [assumption].
% 2.72/2.96  Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex),E,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Complex_Ocomplex).  [resolve(435,a,431,a)].
% 2.76/3.00  Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,hAPP(c_HOL_Otimes__class_Otimes(D,tc_Complex_Ocomplex),E),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Complex_Ocomplex).  [resolve(435,a,432,a)].
% 2.76/3.00  436 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom).  [assumption].
% 2.76/3.00  437 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom).  [assumption].
% 2.76/3.00  438 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom).  [assumption].
% 2.76/3.00  439 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom).  [assumption].
% 2.76/3.00  440 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom).  [assumption].
% 2.76/3.00  441 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom).  [assumption].
% 2.76/3.00  442 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom).  [assumption].
% 2.76/3.00  443 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom).  [assumption].
% 2.76/3.00  444 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom).  [assumption].
% 2.76/3.00  445 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom).  [assumption].
% 2.76/3.00  446 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom).  [assumption].
% 2.76/3.00  447 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom).  [assumption].
% 2.76/3.00  448 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom).  [assumption].
% 2.76/3.00  449 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom).  [assumption].
% 2.76/3.00  450 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom).  [assumption].
% 2.76/3.00  451 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom).  [assumption].
% 2.76/3.00  452 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_0) # label(axiom).  [assumption].
% 2.76/3.00  453 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_1) # label(axiom).  [assumption].
% 2.80/3.05  454 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if__lattice_1) # label(axiom).  [assumption].
% 2.80/3.05  455 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom).  [assumption].
% 2.80/3.05  456 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom).  [assumption].
% 2.80/3.05  Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)).  [resolve(436,a,437,a)].
% 2.80/3.05  Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)).  [resolve(436,a,439,a)].
% 2.80/3.05  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(436,a,443,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_lessequals(A,tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)).  [resolve(436,a,444,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(436,a,446,a)].
% 2.80/3.05  Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B.  [resolve(436,a,450,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)).  [resolve(436,a,451,a)].
% 2.80/3.05  Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(436,a,454,a)].
% 2.80/3.05  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(436,a,455,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)).  [resolve(436,a,456,a)].
% 2.80/3.05  457 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom).  [assumption].
% 2.80/3.05  Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)).  [resolve(457,a,437,a)].
% 2.80/3.05  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)).  [resolve(457,a,443,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)).  [resolve(457,a,444,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)).  [resolve(457,a,446,a)].
% 2.80/3.05  Derived: c_SetInterval_Oord__class_OlessThan(A,tc_Int_Oint) != c_SetInterval_Oord__class_OlessThan(B,tc_Int_Oint) | A = B.  [resolve(457,a,450,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)).  [resolve(457,a,451,a)].
% 2.80/3.05  Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(457,a,454,a)].
% 2.80/3.05  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)).  [resolve(457,a,455,a)].
% 2.80/3.05  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)).  [resolve(457,a,456,a)].
% 2.80/3.05  458 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).  [assumption].
% 2.80/3.05  459 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom).  [assumption].
% 2.80/3.05  460 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom).  [assumption].
% 2.80/3.10  461 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom).  [assumption].
% 2.80/3.10  462 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom).  [assumption].
% 2.80/3.10  463 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom).  [assumption].
% 2.80/3.10  464 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom).  [assumption].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(458,a,459,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(458,a,460,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(458,a,461,a)].
% 2.80/3.10  465 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).  [assumption].
% 2.80/3.10  466 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom).  [assumption].
% 2.80/3.10  467 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A),A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)))) # label(cls_abs__triangle__ineq2_0) # label(axiom).  [assumption].
% 2.80/3.10  468 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__of__nonneg_0) # label(axiom).  [assumption].
% 2.80/3.10  469 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__le__zero__iff_0) # label(axiom).  [assumption].
% 2.80/3.10  470 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)) = hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(C,B,A)) # label(cls_abs__minus__commute_0) # label(axiom).  [assumption].
% 2.80/3.10  471 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),C,A),D)) = hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),C,A),D) # label(cls_abs__setsum__abs_0) # label(axiom).  [assumption].
% 2.80/3.10  472 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C)) # label(cls_abs__le__D1_0) # label(axiom).  [assumption].
% 2.80/3.10  473 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),A),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),C,A),D))) # label(cls_setsum__abs_0) # label(axiom).  [assumption].
% 2.80/3.10  474 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A)),A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)))) # label(cls_abs__triangle__ineq3_0) # label(axiom).  [assumption].
% 2.80/3.10  475 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__le__zero__iff_1) # label(axiom).  [assumption].
% 2.80/3.10  476 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,D,A)),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(C,E,A)),A))) # label(cls_abs__diff__triangle__ineq_0) # label(axiom).  [assumption].
% 2.80/3.10  477 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__idempotent_0) # label(axiom).  [assumption].
% 2.80/3.10  478 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Oplus__class_Oplus(B,C,A)),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A))) # label(cls_abs__triangle__ineq_0) # label(axiom).  [assumption].
% 2.80/3.10  479 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom).  [assumption].
% 2.80/3.10  480 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) # label(cls_abs__ge__self_0) # label(axiom).  [assumption].
% 2.80/3.10  481 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),C,A),D))) # label(cls_setsum__abs__ge__zero_0) # label(axiom).  [assumption].
% 2.80/3.10  482 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__of__pos_0) # label(axiom).  [assumption].
% 2.80/3.10  483 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom).  [assumption].
% 2.80/3.10  484 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__not__less__zero_0) # label(axiom).  [assumption].
% 2.80/3.10  485 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ominus__class_Ominus(B,C,A)),A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A))) # label(cls_abs__triangle__ineq4_0) # label(axiom).  [assumption].
% 2.80/3.10  486 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom).  [assumption].
% 2.80/3.10  487 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),C),A) # label(cls_abs__add__abs_0) # label(axiom).  [assumption].
% 2.80/3.10  488 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)))) # label(cls_zero__less__abs__iff_0) # label(axiom).  [assumption].
% 2.80/3.10  489 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) # label(cls_abs__ge__zero_0) # label(axiom).  [assumption].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)))).  [resolve(466,a,467,a)].
% 2.80/3.10  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(466,a,468,a)].
% 2.80/3.10  Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(466,a,469,a)].
% 2.80/3.10  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,A,tc_Int_Oint)).  [resolve(466,a,470,a)].
% 2.80/3.10  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),B,tc_Int_Oint),C)) = hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),B,tc_Int_Oint),C).  [resolve(466,a,471,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B)).  [resolve(466,a,472,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C)),tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),B,tc_Int_Oint),C))).  [resolve(466,a,473,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint)),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)))).  [resolve(466,a,474,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(466,a,475,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint)),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint)),tc_Int_Oint))).  [resolve(466,a,476,a)].
% 2.80/3.10  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A).  [resolve(466,a,477,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint)),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint))).  [resolve(466,a,478,a)].
% 2.80/3.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(466,a,479,a)].
% 2.90/3.19  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))).  [resolve(466,a,480,a)].
% 2.90/3.19  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),B,tc_Int_Oint),C))).  [resolve(466,a,481,a)].
% 2.90/3.19  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(466,a,482,a)].
% 2.90/3.19  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(466,a,483,a)].
% 2.90/3.19  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(466,a,484,a)].
% 2.90/3.19  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint))).  [resolve(466,a,485,a)].
% 2.90/3.19  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(466,a,486,a)].
% 2.90/3.19  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint).  [resolve(466,a,487,a)].
% 2.90/3.19  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)))).  [resolve(466,a,488,a)].
% 2.90/3.19  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))).  [resolve(466,a,489,a)].
% 2.90/3.19  490 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom).  [assumption].
% 2.90/3.19  491 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom).  [assumption].
% 2.90/3.19  492 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom).  [assumption].
% 2.90/3.19  493 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom).  [assumption].
% 2.90/3.19  494 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
% 2.90/3.19  495 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__right_Oadd_0) # label(axiom).  [assumption].
% 2.90/3.19  496 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult_Oadd__right_0) # label(axiom).  [assumption].
% 2.90/3.19  497 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),D) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult__left_Oadd_0) # label(axiom).  [assumption].
% 2.90/3.19  498 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),D) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult_Oadd__left_0) # label(axiom).  [assumption].
% 2.90/3.19  499 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom).  [assumption].
% 2.90/3.19  500 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osuminf_0) # label(axiom).  [assumption].
% 2.90/3.19  501 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Series_Osuminf(C,A)) | -c_Series_Osummable(C,A) # label(cls_suminf__mult_0) # label(axiom).  [assumption].
% 2.90/3.19  502 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Finite__Set_Osetsum(C,D,A),E)) = hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,D),D,A),E) # label(cls_mult__right_Osetsum_0) # label(axiom).  [assumption].
% 2.90/3.19  503 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_summable__mult_0) # label(axiom).  [assumption].
% 2.90/3.19  504 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osummable_0) # label(axiom).  [assumption].
% 2.90/3.19  505 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_Series_Osums(C,D,A) # label(cls_mult__right_Osums_0) # label(axiom).  [assumption].
% 2.90/3.19  506 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_Series_Osums(C,D,A) # label(cls_sums__mult_0) # label(axiom).  [assumption].
% 2.90/3.19  507 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),A),c_HOL_Ominus__class_Ominus(C,E,A)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),A),E),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),c_HOL_Ominus__class_Ominus(C,E,A)),A) # label(cls_mult_Oprod__diff__prod_0) # label(axiom).  [assumption].
% 2.90/3.19  508 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__right_Odiff_0) # label(axiom).  [assumption].
% 2.90/3.19  509 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult_Odiff__right_0) # label(axiom).  [assumption].
% 2.90/3.19  510 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),A),D) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult_Odiff__left_0) # label(axiom).  [assumption].
% 2.90/3.19  511 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),A),D) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult__left_Odiff_0) # label(axiom).  [assumption].
% 2.90/3.19  512 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom).  [assumption].
% 2.90/3.19  513 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom).  [assumption].
% 2.96/3.24  514 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom).  [assumption].
% 2.96/3.24  515 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom).  [assumption].
% 2.96/3.24  Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex).  [resolve(494,a,499,a)].
% 2.96/3.24  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex).  [resolve(494,a,500,a)].
% 2.96/3.24  Derived: c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Series_Osuminf(B,tc_Complex_Ocomplex)) | -c_Series_Osummable(B,tc_Complex_Ocomplex).  [resolve(494,a,501,a)].
% 2.96/3.24  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_Finite__Set_Osetsum(B,C,tc_Complex_Ocomplex),D)) = hAPP(c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,C),C,tc_Complex_Ocomplex),D).  [resolve(494,a,502,a)].
% 2.96/3.24  Derived: c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex).  [resolve(494,a,503,a)].
% 2.96/3.24  Derived: c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex).  [resolve(494,a,505,a)].
% 2.96/3.24  Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),D),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex)),tc_Complex_Ocomplex).  [resolve(494,a,507,a)].
% 2.96/3.24  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(494,a,508,a)].
% 2.96/3.24  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex).  [resolve(494,a,510,a)].
% 2.96/3.24  516 class_RealVector_Ometric__space(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Ometric__space) # label(axiom).  [assumption].
% 2.96/3.24  517 -class_RealVector_Ometric__space(A) | B = C | -c_SEQ_OLIMSEQ(D,C,A) | -c_SEQ_OLIMSEQ(D,B,A) # label(cls_LIMSEQ__unique_0) # label(axiom).  [assumption].
% 2.96/3.24  518 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Suc_0) # label(axiom).  [assumption].
% 2.96/3.24  519 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_LIMSEQ__Suc__iff_0) # label(axiom).  [assumption].
% 3.04/3.28  520 -class_RealVector_Ometric__space(A) | c_SEQ_Olim(B,A) = C | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_limI_0) # label(axiom).  [assumption].
% 3.04/3.28  521 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(B,c_SEQ_Olim(B,A),A) | -c_SEQ_Oconvergent(B,A) # label(cls_convergent__LIMSEQ__iff_0) # label(axiom).  [assumption].
% 3.04/3.28  522 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(B,A) | -c_SEQ_OLIMSEQ(B,c_SEQ_Olim(B,A),A) # label(cls_convergent__LIMSEQ__iff_1) # label(axiom).  [assumption].
% 3.04/3.28  523 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(B,A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_convergent__def_1) # label(axiom).  [assumption].
% 3.04/3.28  524 -class_RealVector_Ometric__space(A) | c_SEQ_Oconvergent(B,A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_convergentI_0) # label(axiom).  [assumption].
% 3.04/3.28  Derived: A = B | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,A,tc_Complex_Ocomplex).  [resolve(516,a,517,a)].
% 3.04/3.28  Derived: c_SEQ_OLIMSEQ(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex).  [resolve(516,a,518,a)].
% 3.04/3.28  Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex).  [resolve(516,a,519,a)].
% 3.04/3.28  Derived: c_SEQ_Olim(A,tc_Complex_Ocomplex) = B | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex).  [resolve(516,a,520,a)].
% 3.04/3.28  Derived: c_SEQ_OLIMSEQ(A,c_SEQ_Olim(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_Oconvergent(A,tc_Complex_Ocomplex).  [resolve(516,a,521,a)].
% 3.04/3.28  Derived: c_SEQ_Oconvergent(A,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,c_SEQ_Olim(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(516,a,522,a)].
% 3.04/3.28  Derived: c_SEQ_Oconvergent(A,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex).  [resolve(516,a,523,a)].
% 3.04/3.28  525 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom).  [assumption].
% 3.04/3.28  526 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom).  [assumption].
% 3.04/3.28  527 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom).  [assumption].
% 3.04/3.28  528 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom).  [assumption].
% 3.04/3.28  529 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom).  [assumption].
% 3.04/3.28  530 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom).  [assumption].
% 3.04/3.28  531 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom).  [assumption].
% 3.04/3.28  532 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom).  [assumption].
% 3.04/3.28  533 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom).  [assumption].
% 3.04/3.28  534 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom).  [assumption].
% 3.04/3.28  535 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom).  [assumption].
% 3.04/3.28  536 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom).  [assumption].
% 3.04/3.28  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(525,a,526,a)].
% 3.04/3.28  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(525,a,527,a)].
% 3.04/3.28  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(525,a,528,a)].
% 3.04/3.28  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(525,a,529,a)].
% 3.04/3.28  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(525,a,531,a)].
% 3.04/3.28  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(525,a,532,a)].
% 3.04/3.28  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)).  [resolve(525,a,533,a)].
% 3.04/3.28  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(525,a,534,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(525,a,536,a)].
% 3.08/3.33  537 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom).  [assumption].
% 3.08/3.33  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(537,a,526,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(537,a,527,a)].
% 3.08/3.33  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(537,a,528,a)].
% 3.08/3.33  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(537,a,529,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(537,a,531,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(537,a,532,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)).  [resolve(537,a,533,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(537,a,534,a)].
% 3.08/3.33  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(537,a,536,a)].
% 3.08/3.33  538 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom).  [assumption].
% 3.08/3.33  539 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom).  [assumption].
% 3.12/3.37  540 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom).  [assumption].
% 3.12/3.37  541 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom).  [assumption].
% 3.12/3.37  542 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom).  [assumption].
% 3.12/3.37  543 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom).  [assumption].
% 3.12/3.37  544 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom).  [assumption].
% 3.12/3.37  545 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom).  [assumption].
% 3.12/3.37  546 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom).  [assumption].
% 3.12/3.37  547 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom).  [assumption].
% 3.12/3.37  548 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom).  [assumption].
% 3.12/3.37  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint))).  [resolve(538,a,541,a)].
% 3.12/3.37  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint))).  [resolve(538,a,543,a)].
% 3.12/3.37  Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(538,a,545,a)].
% 3.12/3.37  Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(538,a,547,a)].
% 3.12/3.37  549 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom).  [assumption].
% 3.12/3.37  550 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_Odiff_0) # label(axiom).  [assumption].
% 3.12/3.37  551 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_Oadd_0) # label(axiom).  [assumption].
% 3.32/3.57  552 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom).  [assumption].
% 3.32/3.57  553 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom).  [assumption].
% 3.32/3.57  554 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ominus__class_Ominus(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__diff_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint).  [resolve(553,a,554,a)].
% 3.32/3.57  555 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex).  [resolve(555,a,554,a)].
% 3.32/3.57  556 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom).  [assumption].
% 3.32/3.57  557 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom).  [assumption].
% 3.32/3.57  558 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom).  [assumption].
% 3.32/3.57  559 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom).  [assumption].
% 3.32/3.57  560 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom).  [assumption].
% 3.32/3.57  561 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B.  [resolve(560,a,561,a)].
% 3.32/3.57  562 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B.  [resolve(562,a,561,a)].
% 3.32/3.57  563 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B.  [resolve(563,a,561,a)].
% 3.32/3.57  564 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom).  [assumption].
% 3.32/3.57  565 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),D),A) # label(cls_right__diff__distrib__number__of_0) # label(axiom).  [assumption].
% 3.32/3.57  566 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),A),C),E,A),A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),E,A) # label(cls_eq__add__iff2_1) # label(axiom).  [assumption].
% 3.32/3.57  567 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),A),c_Int_Onumber__class_Onumber__of(D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Int_Onumber__class_Onumber__of(D,A)),hAPP(c_HOL_Otimes__class_Otimes(C,A),c_Int_Onumber__class_Onumber__of(D,A)),A) # label(cls_left__diff__distrib__number__of_0) # label(axiom).  [assumption].
% 3.32/3.57  568 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),A),C),D,A),A) # label(cls_eq__add__iff1_1) # label(axiom).  [assumption].
% 3.32/3.57  569 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),A),C),D,A) = F # label(cls_eq__add__iff1_0) # label(axiom).  [assumption].
% 3.32/3.57  570 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(E,A),C),F,A) | D = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),A),C),F,A) # label(cls_eq__add__iff2_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),B),hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),C),tc_Int_Oint).  [resolve(564,a,565,a)].
% 3.32/3.57  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint),tc_Int_Oint),B),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),D,tc_Int_Oint).  [resolve(564,a,566,a)].
% 3.32/3.57  Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)) = c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)),tc_Int_Oint).  [resolve(564,a,567,a)].
% 3.32/3.57  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),tc_Int_Oint),B),C,tc_Int_Oint),tc_Int_Oint).  [resolve(564,a,568,a)].
% 3.32/3.57  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),tc_Int_Oint),B),C,tc_Int_Oint) = E.  [resolve(564,a,569,a)].
% 3.32/3.57  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Int_Oint),B),E,tc_Int_Oint) | C = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),tc_Int_Oint),B),E,tc_Int_Oint).  [resolve(564,a,570,a)].
% 3.38/3.65  571 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom).  [assumption].
% 3.38/3.65  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),D,tc_Complex_Ocomplex).  [resolve(571,a,566,a)].
% 3.38/3.65  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Complex_Ocomplex),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(571,a,568,a)].
% 3.38/3.65  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Complex_Ocomplex),B),E,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) = E.  [resolve(571,a,569,a)].
% 3.38/3.65  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,tc_Complex_Ocomplex),B),E,tc_Complex_Ocomplex) | C = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),E,tc_Complex_Ocomplex).  [resolve(571,a,570,a)].
% 3.38/3.65  572 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom).  [assumption].
% 3.38/3.65  573 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),D) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom).  [assumption].
% 3.38/3.65  574 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom).  [assumption].
% 3.38/3.65  575 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom).  [assumption].
% 3.38/3.65  576 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom).  [assumption].
% 3.38/3.65  577 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom).  [assumption].
% 3.38/3.65  578 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom).  [assumption].
% 3.38/3.65  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(576,a,577,a)].
% 3.38/3.65  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(576,a,578,a)].
% 3.50/3.77  579 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom).  [assumption].
% 3.50/3.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(579,a,577,a)].
% 3.50/3.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(579,a,578,a)].
% 3.50/3.77  580 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  581 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C.  [resolve(580,a,581,a)].
% 3.50/3.77  582 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C.  [resolve(582,a,581,a)].
% 3.50/3.77  583 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C.  [resolve(583,a,581,a)].
% 3.50/3.77  584 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  585 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom).  [assumption].
% 3.50/3.77  586 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C.  [resolve(584,a,586,a)].
% 3.50/3.77  587 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C.  [resolve(587,a,586,a)].
% 3.50/3.77  588 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.50/3.77  Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C.  [resolve(588,a,586,a)].
% 3.50/3.77  589 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom).  [assumption].
% 3.50/3.77  590 -class_Ring__and__Field_Olordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)))) # label(cls_abs__le__mult_0) # label(axiom).  [assumption].
% 3.50/3.77  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B)),tc_Int_Oint),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)))).  [resolve(589,a,590,a)].
% 3.64/3.88  591 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 3.64/3.88  592 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),A),B) = B # label(cls_mult__1_0) # label(axiom).  [assumption].
% 3.64/3.88  593 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(B,A),D),A),hAPP(c_Power_Opower__class_Opower(C,A),D)) # label(cls_power__mult__distrib_0) # label(axiom).  [assumption].
% 3.64/3.88  594 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 3.64/3.89  595 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom).  [assumption].
% 3.64/3.89  596 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom).  [assumption].
% 3.64/3.89  597 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom).  [assumption].
% 3.64/3.89  598 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom).  [assumption].
% 3.64/3.89  599 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom).  [assumption].
% 3.64/3.89  600 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom).  [assumption].
% 3.64/3.89  601 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom).  [assumption].
% 3.64/3.89  602 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom).  [assumption].
% 3.64/3.89  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A.  [resolve(596,a,597,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A.  [resolve(596,a,598,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(596,a,599,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A.  [resolve(596,a,600,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B.  [resolve(596,a,602,a)].
% 3.64/3.89  603 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom).  [assumption].
% 3.64/3.89  Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A.  [resolve(603,a,597,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A.  [resolve(603,a,598,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(603,a,599,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A.  [resolve(603,a,600,a)].
% 3.64/3.89  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B.  [resolve(603,a,602,a)].
% 3.64/3.89  604 class_Power_Opower(tc_nat) # label(clsarity_nat__Power_Opower) # label(axiom).  [assumption].
% 3.64/3.89  605 -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_power__Suc_0) # label(axiom).  [assumption].
% 3.64/3.89  606 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom).  [assumption].
% 3.64/3.89  607 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Suc,B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom).  [assumption].
% 3.64/3.89  608 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom).  [assumption].
% 3.64/3.89  609 -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0_0) # label(axiom).  [assumption].
% 3.64/3.89  610 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom).  [assumption].
% 3.64/3.89  611 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left__number__of_1) # label(axiom).  [assumption].
% 3.64/3.89  612 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom).  [assumption].
% 3.64/3.89  613 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom).  [assumption].
% 3.64/3.89  614 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom).  [assumption].
% 3.64/3.89  615 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom).  [assumption].
% 3.64/3.89  616 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom).  [assumption].
% 3.64/3.89  617 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom).  [assumption].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_nat).  [resolve(604,a,606,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,607,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,608,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,610,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,611,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(B,tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,613,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,614,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,615,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,616,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(604,a,617,d)].
% 3.64/3.89  618 class_Power_Opower(tc_Int_Oint) # label(clsarity_Int__Oint__Power_Opower) # label(axiom).  [assumption].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint).  [resolve(618,a,606,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(618,a,607,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(618,a,608,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(618,a,610,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(618,a,611,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(618,a,613,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(618,a,614,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(618,a,615,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(618,a,616,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(618,a,617,d)].
% 3.64/3.89  619 class_Power_Opower(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Power_Opower) # label(axiom).  [assumption].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).  [resolve(619,a,606,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(619,a,607,b)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(619,a,608,d)].
% 3.64/3.89  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(619,a,610,d)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(619,a,611,b)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(619,a,613,d)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(619,a,614,b)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(619,a,615,d)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(619,a,616,d)].
% 3.64/3.93  Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(619,a,617,d)].
% 3.64/3.93  620 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom).  [assumption].
% 3.64/3.93  621 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != c_HOL_Oplus__class_Oplus(C,E,A) | c_HOL_Oplus__class_Oplus(B,D,A) = E # label(cls_add__cancel__21_0) # label(axiom).  [assumption].
% 3.64/3.93  622 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__cancel__21_1) # label(axiom).  [assumption].
% 3.64/3.93  623 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom).  [assumption].
% 3.64/3.93  624 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom).  [assumption].
% 3.64/3.93  625 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom).  [assumption].
% 3.64/3.93  626 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom).  [assumption].
% 3.64/3.93  627 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom).  [assumption].
% 3.64/3.93  628 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),E)),A) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) # label(cls_setsum__diff__nat__ivl_0) # label(axiom).  [assumption].
% 3.73/3.97  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) = D.  [resolve(620,a,621,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint) | B = C.  [resolve(620,a,623,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,C,tc_Int_Oint) | A = B.  [resolve(620,a,624,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint),tc_Int_Oint).  [resolve(620,a,625,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)),tc_Int_Oint) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)).  [resolve(620,a,628,a)].
% 3.73/3.97  629 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom).  [assumption].
% 3.73/3.97  Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) = D.  [resolve(629,a,621,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex) | B = C.  [resolve(629,a,623,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(C,C,tc_Complex_Ocomplex) | A = B.  [resolve(629,a,624,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex).  [resolve(629,a,625,a)].
% 3.73/3.97  Derived: c_HOL_Ominus__class_Ominus(hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)),tc_Complex_Ocomplex) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)).  [resolve(629,a,628,a)].
% 3.73/3.97  630 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom).  [assumption].
% 3.73/3.97  631 -class_RealVector_Oreal__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A),F,A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(C,E,A),F,A)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,A),F,A),A),E),A) # label(cls_DERIV__mult__lemma_0) # label(axiom).  [assumption].
% 3.73/3.97  Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D),tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex)),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex),tc_Complex_Ocomplex),D),tc_Complex_Ocomplex).  [resolve(630,a,631,a)].
% 3.73/4.01  632 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom).  [assumption].
% 3.73/4.01  633 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__summable_0) # label(axiom).  [assumption].
% 3.73/4.01  634 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__iff_0) # label(axiom).  [assumption].
% 3.73/4.01  635 -class_RealVector_Oreal__normed__vector(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | c_Series_Osums(B,C,A) | -c_Series_Osums(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc__imp_0) # label(axiom).  [assumption].
% 3.73/4.01  636 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),c_Series_Osuminf(B,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__sumr__LIMSEQ__suminf_0) # label(axiom).  [assumption].
% 3.73/4.01  637 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,c_HOL_Ozero__class_Ozero(A),A) | -c_Series_Osummable(B,A) # label(cls_summable__LIMSEQ__zero_0) # label(axiom).  [assumption].
% 3.73/4.01  638 -class_RealVector_Oreal__normed__vector(A) | B = c_Series_Osuminf(C,A) | -c_Series_Osums(C,B,A) # label(cls_sums__unique_0) # label(axiom).  [assumption].
% 3.73/4.01  639 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osuminf(B,A) = C | -c_Series_Osums(B,C,A) # label(cls_sums__iff_1) # label(axiom).  [assumption].
% 3.73/4.01  640 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__sums_0) # label(axiom).  [assumption].
% 3.73/4.01  641 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osummable(B,A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) # label(cls_sums__iff_2) # label(axiom).  [assumption].
% 3.73/4.01  642 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,c_HOL_Oplus__class_Oplus(C,hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)),A),A) | -c_Series_Osums(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc_0) # label(axiom).  [assumption].
% 3.73/4.01  643 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osuminf(B,A) = c_SEQ_Olim(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),A) # label(cls_suminf__eq__lim_0) # label(axiom).  [assumption].
% 3.73/4.01  644 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),C,A) | -c_Series_Osums(B,C,A) # label(cls_sums__def_0) # label(axiom).  [assumption].
% 3.73/4.01  645 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),C,A) # label(cls_sums__def_1) # label(axiom).  [assumption].
% 3.73/4.01  646 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_SEQ_Oconvergent(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),A) # label(cls_summable__convergent__sumr__iff_1) # label(axiom).  [assumption].
% 3.73/4.01  647 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_Oconvergent(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),A,tc_nat),A) | -c_Series_Osummable(B,A) # label(cls_summable__convergent__sumr__iff_0) # label(axiom).  [assumption].
% 3.73/4.01  648 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)),A) | hBOOL(hAPP(c_lessequals(C,tc_nat),c_Series_Osko__Series__Xseries__zero__1__1(B,C,A))) # label(cls_series__zero_0) # label(axiom).  [assumption].
% 3.73/4.01  649 -class_RealVector_Oreal__normed__vector(A) | hAPP(B,c_Series_Osko__Series__Xseries__zero__1__1(B,C,A)) != c_HOL_Ozero__class_Ozero(A) | c_Series_Osums(B,hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)),A) # label(cls_series__zero_1) # label(axiom).  [assumption].
% 3.73/4.01  Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex).  [resolve(632,a,633,a)].
% 3.73/4.01  Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Series_Osums(A,B,tc_Complex_Ocomplex) | -c_Series_Osums(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex).  [resolve(632,a,635,a)].
% 3.73/4.01  Derived: c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),c_Series_Osuminf(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex).  [resolve(632,a,636,a)].
% 3.73/4.01  Derived: c_SEQ_OLIMSEQ(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex).  [resolve(632,a,637,a)].
% 3.73/4.01  Derived: A = c_Series_Osuminf(B,tc_Complex_Ocomplex) | -c_Series_Osums(B,A,tc_Complex_Ocomplex).  [resolve(632,a,638,a)].
% 3.73/4.01  Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = B | -c_Series_Osums(A,B,tc_Complex_Ocomplex).  [resolve(632,a,639,a)].
% 3.73/4.01  Derived: c_Series_Osums(A,c_Series_Osuminf(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex).  [resolve(632,a,640,a)].
% 3.73/4.01  Derived: c_Series_Osums(A,c_HOL_Oplus__class_Oplus(B,hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osums(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex).  [resolve(632,a,642,a)].
% 3.73/4.01  Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = c_SEQ_Olim(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex).  [resolve(632,a,643,a)].
% 3.73/4.01  Derived: c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex).  [resolve(632,a,644,a)].
% 3.73/4.01  Derived: c_Series_Osums(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex).  [resolve(632,a,645,a)].
% 3.73/4.01  Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_SEQ_Oconvergent(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex).  [resolve(632,a,646,a)].
% 3.73/4.01  Derived: c_SEQ_Oconvergent(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex).  [resolve(632,a,647,a)].
% 3.73/4.01  Derived: c_Series_Osums(A,hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)),tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(B,tc_nat),c_Series_Osko__Series__Xseries__zero__1__1(A,B,tc_Complex_Ocomplex))).  [resolve(632,a,648,a)].
% 3.83/4.13  Derived: hAPP(A,c_Series_Osko__Series__Xseries__zero__1__1(A,B,tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Series_Osums(A,hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)),tc_Complex_Ocomplex).  [resolve(632,a,649,a)].
% 3.83/4.13  650 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.83/4.13  651 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom).  [assumption].
% 3.83/4.13  652 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.83/4.13  653 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 3.83/4.13  654 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom).  [assumption].
% 3.83/4.13  655 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),C),hAPP(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),A),D),A) # label(cls_right__distrib__number__of_0) # label(axiom).  [assumption].
% 3.83/4.13  656 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),E,A),A) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),A),C),E,A) # label(cls_combine__common__factor_0) # label(axiom).  [assumption].
% 3.83/4.13  657 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),A),c_Int_Onumber__class_Onumber__of(D,A)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Int_Onumber__class_Onumber__of(D,A)),hAPP(c_HOL_Otimes__class_Otimes(C,A),c_Int_Onumber__class_Onumber__of(D,A)),A) # label(cls_left__distrib__number__of_0) # label(axiom).  [assumption].
% 3.83/4.13  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat),B),D,tc_nat).  [resolve(654,a,656,a)].
% 3.83/4.13  658 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom).  [assumption].
% 3.83/4.13  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Int_Oint),B),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint),B),D,tc_Int_Oint).  [resolve(658,a,656,a)].
% 3.83/4.13  659 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom).  [assumption].
% 3.83/4.13  Derived: c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),B),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),D,tc_Complex_Ocomplex).  [resolve(659,a,656,a)].
% 3.83/4.13  660 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom).  [assumption].
% 3.83/4.13  661 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom).  [assumption].
% 4.01/4.24  Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B.  [resolve(660,a,661,a)].
% 4.01/4.24  662 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom).  [assumption].
% 4.01/4.24  Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | A = B.  [resolve(662,a,661,a)].
% 4.01/4.24  663 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom).  [assumption].
% 4.01/4.24  664 -class_RealVector_Oreal__normed__div__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Oinverse__class_Oinverse(A),B,A,A,tc_nat),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) | C = c_HOL_Ozero__class_Ozero(A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__inverse_0) # label(axiom).  [assumption].
% 4.01/4.24  Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex).  [resolve(663,a,664,a)].
% 4.01/4.24  665 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom).  [assumption].
% 4.01/4.24  666 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom).  [assumption].
% 4.01/4.24  667 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom).  [assumption].
% 4.01/4.24  668 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 4.01/4.24  669 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom).  [assumption].
% 4.01/4.24  670 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom).  [assumption].
% 4.01/4.24  671 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom).  [assumption].
% 4.01/4.24  672 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom).  [assumption].
% 4.01/4.24  673 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom).  [assumption].
% 4.01/4.24  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(668,a,669,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(668,a,670,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(668,a,671,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(668,a,672,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(668,a,673,a)].
% 4.03/4.32  674 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(674,a,669,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)).  [resolve(674,a,670,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(674,a,671,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)).  [resolve(674,a,672,a)].
% 4.03/4.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)).  [resolve(674,a,673,a)].
% 4.03/4.32  675 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 4.03/4.32  676 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom).  [assumption].
% 4.03/4.32  677 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom).  [assumption].
% 4.03/4.32  678 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom).  [assumption].
% 4.03/4.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Int_Oint),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(675,a,678,a)].
% 4.03/4.32  679 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 4.03/4.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(679,a,678,a)].
% 4.03/4.32  680 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 4.38/4.61  681 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom).  [assumption].
% 4.38/4.61  682 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom).  [assumption].
% 4.38/4.61  683 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 4.38/4.61  684 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 4.38/4.61  685 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom).  [assumption].
% 4.38/4.61  686 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if_1) # label(axiom).  [assumption].
% 4.38/4.61  Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))).  [resolve(685,a,686,a)].
% 4.38/4.61  687 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom).  [assumption].
% 4.38/4.61  688 -class_Ring__and__Field_Oring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(B,C,tc_nat),A) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) # label(cls_of__nat__diff_0) # label(axiom).  [assumption].
% 4.38/4.61  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(687,a,688,a)].
% 4.38/4.61  689 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom).  [assumption].
% 4.38/4.61  Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(689,a,688,a)].
% 4.38/4.61  690 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
% 4.38/4.61  691 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom).  [assumption].
% 4.38/4.61  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint).  [resolve(690,a,691,a)].
% 4.38/4.61  692 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom).  [assumption].
% 4.38/4.61  Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).  [resolve(692,a,691,a)].
% 4.38/4.61  693 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom).  [assumption].
% 4.38/4.61  694 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom).  [assumption].
% 4.38/4.61  Derived: A = A.  [resolve(693,b,694,a)].
% 4.38/4.61  
% 4.38/4.61  ============================== end predicate elimination =============
% 4.38/4.61  
% 4.38/4.61  Auto_denials:  (non-Horn, no changes).
% 4.38/4.61  
% 4.38/4.61  Term ordering decisions:
% 4.38/4.61  Function symbol KB weights:  tc_nat=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. c_Suc=1. tc_bool=1. t_a=1. v_n=1. tc_String_Ochar=1. v_k=1. c_Complex_Oii=1. hAPP=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_Power_Opower__class_Opower=1. c_Int_Onumber__class_Onumber__of=1. c_SetInterval_Oord__claCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------