%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWV581-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n005.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 21:13:58 EDT 2022

% Result   : Timeout 300.04s 300.40s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV581-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jun 15 07:25:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.44/1.69  ============================== Prover9 ===============================
% 1.44/1.69  Prover9 (32) version 2009-11A, November 2009.
% 1.44/1.69  Process 29383 was started by sandbox2 on n005.cluster.edu,
% 1.44/1.69  Wed Jun 15 07:25:40 2022
% 1.44/1.69  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29229_n005.cluster.edu".
% 1.44/1.69  ============================== end of head ===========================
% 1.44/1.69  
% 1.44/1.69  ============================== INPUT =================================
% 1.44/1.69  
% 1.44/1.69  % Reading from file /tmp/Prover9_29229_n005.cluster.edu
% 1.44/1.69  
% 1.44/1.69  set(prolog_style_variables).
% 1.44/1.69  set(auto2).
% 1.44/1.69      % set(auto2) -> set(auto).
% 1.44/1.69      % set(auto) -> set(auto_inference).
% 1.44/1.69      % set(auto) -> set(auto_setup).
% 1.44/1.69      % set(auto_setup) -> set(predicate_elim).
% 1.44/1.69      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.44/1.69      % set(auto) -> set(auto_limits).
% 1.44/1.69      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.44/1.69      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.44/1.69      % set(auto) -> set(auto_denials).
% 1.44/1.69      % set(auto) -> set(auto_process).
% 1.44/1.69      % set(auto2) -> assign(new_constants, 1).
% 1.44/1.69      % set(auto2) -> assign(fold_denial_max, 3).
% 1.44/1.69      % set(auto2) -> assign(max_weight, "200.000").
% 1.44/1.69      % set(auto2) -> assign(max_hours, 1).
% 1.44/1.69      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.44/1.69      % set(auto2) -> assign(max_seconds, 0).
% 1.44/1.69      % set(auto2) -> assign(max_minutes, 5).
% 1.44/1.69      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.44/1.69      % set(auto2) -> set(sort_initial_sos).
% 1.44/1.69      % set(auto2) -> assign(sos_limit, -1).
% 1.44/1.69      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.44/1.69      % set(auto2) -> assign(max_megs, 400).
% 1.44/1.69      % set(auto2) -> assign(stats, some).
% 1.44/1.69      % set(auto2) -> clear(echo_input).
% 1.44/1.69      % set(auto2) -> set(quiet).
% 1.44/1.69      % set(auto2) -> clear(print_initial_clauses).
% 1.44/1.69      % set(auto2) -> clear(print_given).
% 1.44/1.69  assign(lrs_ticks,-1).
% 1.44/1.69  assign(sos_limit,10000).
% 1.44/1.69  assign(order,kbo).
% 1.44/1.69  set(lex_order_vars).
% 1.44/1.69  clear(print_given).
% 1.44/1.69  
% 1.44/1.69  % formulas(sos).  % not echoed (1173 formulas)
% 1.44/1.69  
% 1.44/1.69  ============================== end of input ==========================
% 1.44/1.69  
% 1.44/1.69  % From the command line: assign(max_seconds, 300).
% 1.44/1.69  
% 1.44/1.69  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.44/1.69  
% 1.44/1.69  % Formulas that are not ordinary clauses:
% 1.44/1.69  
% 1.44/1.69  ============================== end of process non-clausal formulas ===
% 1.44/1.69  
% 1.44/1.69  ============================== PROCESS INITIAL CLAUSES ===============
% 1.44/1.69  
% 1.44/1.69  ============================== PREDICATE ELIMINATION =================
% 1.44/1.69  1 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom).  [assumption].
% 1.44/1.69  2 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__eq__neg_1) # label(axiom).  [assumption].
% 1.44/1.69  3 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) # label(cls_le__eq__neg_0) # label(axiom).  [assumption].
% 1.44/1.69  4 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sup__eq__if_1) # label(axiom).  [assumption].
% 1.44/1.69  5 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sup__0__imp__0_0) # label(axiom).  [assumption].
% 1.44/1.69  6 -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom).  [assumption].
% 1.44/1.69  7 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -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].
% 1.44/1.69  8 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_neg__sup__eq__inf_0) # label(axiom).  [assumption].
% 1.44/1.69  9 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),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].
% 1.44/1.69  10 -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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom).  [assumption].
% 1.44/1.69  11 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)) # label(cls_add__eq__inf__sup_0) # label(axiom).  [assumption].
% 1.44/1.69  12 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sup__eq__if_0) # label(axiom).  [assumption].
% 1.44/1.69  13 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inf__0__imp__0_0) # label(axiom).  [assumption].
% 1.44/1.69  14 -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom).  [assumption].
% 1.44/1.69  15 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -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].
% 1.44/1.69  16 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__self__iff_0) # label(axiom).  [assumption].
% 1.44/1.69  17 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__minus__self__iff_1) # label(axiom).  [assumption].
% 1.44/1.69  18 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) # label(cls_minus__le__self__iff_0) # label(axiom).  [assumption].
% 1.44/1.69  19 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_minus__le__self__iff_1) # label(axiom).  [assumption].
% 1.44/1.69  20 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)) # label(cls_inf__eq__neg__sup_0) # label(axiom).  [assumption].
% 1.44/1.69  21 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_neg__inf__eq__sup_0) # label(axiom).  [assumption].
% 1.44/1.69  22 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) # label(axiom).  [assumption].
% 1.44/1.69  23 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) # label(axiom).  [assumption].
% 1.44/1.69  24 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom).  [assumption].
% 1.44/1.69  25 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),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].
% 1.44/1.69  26 -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)) # label(cls_sup__eq__neg__inf_0) # label(axiom).  [assumption].
% 1.44/1.69  27 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom).  [assumption].
% 1.44/1.69  28 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom).  [assumption].
% 1.44/1.69  29 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) # label(axiom).  [assumption].
% 1.44/1.69  30 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) # label(axiom).  [assumption].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,2,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))).  [resolve(1,a,3,a)].
% 1.44/1.69  Derived: -class_Orderings_Olinorder(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,4,b)].
% 1.44/1.69  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1,a,5,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))).  [resolve(1,a,6,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(1,a,7,a)].
% 1.44/1.69  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal).  [resolve(1,a,8,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,9,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,10,a)].
% 1.44/1.69  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal)),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal)).  [resolve(1,a,11,a)].
% 1.44/1.69  Derived: -class_Orderings_Olinorder(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,12,b)].
% 1.44/1.69  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1,a,13,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))).  [resolve(1,a,14,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(1,a,15,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(1,a,16,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,17,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),A)).  [resolve(1,a,18,a)].
% 1.44/1.69  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(1,a,19,a)].
% 1.44/1.74  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal)).  [resolve(1,a,20,a)].
% 1.44/1.74  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal).  [resolve(1,a,21,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal).  [resolve(1,a,22,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal)),C) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal).  [resolve(1,a,23,a)].
% 1.44/1.74  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,24,a)].
% 1.44/1.74  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(1,a,25,a)].
% 1.44/1.74  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal)).  [resolve(1,a,26,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1,a,27,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(1,a,28,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal).  [resolve(1,a,29,a)].
% 1.44/1.74  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal)),C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal).  [resolve(1,a,30,a)].
% 1.44/1.74  31 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom).  [assumption].
% 1.44/1.74  32 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__right_0) # label(axiom).  [assumption].
% 1.44/1.74  33 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) # label(cls_minus__mult__left_0) # label(axiom).  [assumption].
% 1.44/1.74  34 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I21_J_0) # label(axiom).  [assumption].
% 1.44/1.74  35 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I22_J_0) # label(axiom).  [assumption].
% 1.44/1.74  36 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),C) # label(cls_minus__mult__minus_0) # label(axiom).  [assumption].
% 1.44/1.74  37 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B),A),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),E) # label(cls_eq__add__iff2_1) # label(axiom).  [assumption].
% 1.44/1.74  38 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom).  [assumption].
% 1.44/1.74  39 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom).  [assumption].
% 1.44/1.74  40 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F) # label(cls_eq__add__iff2_0) # label(axiom).  [assumption].
% 1.44/1.74  41 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I20_J_0) # label(axiom).  [assumption].
% 1.44/1.74  42 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I19_J_0) # label(axiom).  [assumption].
% 1.44/1.74  43 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__commute_0) # label(axiom).  [assumption].
% 1.44/1.74  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)).  [resolve(31,a,32,a)].
% 1.44/1.74  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B).  [resolve(31,a,33,a)].
% 1.44/1.74  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(31,a,34,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(31,a,35,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B).  [resolve(31,a,36,a)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),D).  [resolve(31,a,37,a)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C)).  [resolve(31,a,38,a)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C) = E.  [resolve(31,a,39,a)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E).  [resolve(31,a,40,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(31,a,41,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(31,a,42,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)).  [resolve(31,a,43,a)].
% 1.53/1.79  44 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom).  [assumption].
% 1.53/1.79  45 -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].
% 1.53/1.79  46 -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].
% 1.53/1.79  47 -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].
% 1.53/1.79  48 -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].
% 1.53/1.79  49 -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].
% 1.53/1.79  50 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_minus__divide__right_0) # label(axiom).  [assumption].
% 1.53/1.79  51 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) # label(cls_minus__divide__left_0) # label(axiom).  [assumption].
% 1.53/1.79  52 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),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].
% 1.53/1.79  53 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom).  [assumption].
% 1.53/1.79  54 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oinverse__class_Odivide(C,D,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom).  [assumption].
% 1.53/1.79  55 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),D) = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_1) # label(axiom).  [assumption].
% 1.53/1.79  56 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(B)) = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_2) # label(axiom).  [assumption].
% 1.53/1.79  57 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(B)),D) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__zero__left_0) # label(axiom).  [assumption].
% 1.53/1.79  58 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(c_HOL_Ouminus__class_Ouminus(B),D)),E) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(C,D),E)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__minus__left_0) # label(axiom).  [assumption].
% 1.53/1.79  59 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__zero__right_0) # label(axiom).  [assumption].
% 1.53/1.79  60 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),D) = hAPP(hAPP(C,c_HOL_Ozero__class_Ozero(A)),E) # label(cls_vector__space_Oscale__cancel__left_1) # label(axiom).  [assumption].
% 1.53/1.79  61 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(c_HOL_Ouminus__class_Ouminus(A),E)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(C,D),E)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__minus__right_0) # label(axiom).  [assumption].
% 1.53/1.79  62 -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(B) | -c_RealVector_Ovector__space(C,A,B) | hAPP(hAPP(C,D),c_HOL_Ozero__class_Ozero(B)) = hAPP(hAPP(C,E),c_HOL_Ozero__class_Ozero(B)) # label(cls_vector__space_Oscale__cancel__right_1) # label(axiom).  [assumption].
% 1.53/1.79  63 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom).  [assumption].
% 1.53/1.79  64 -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].
% 1.53/1.79  65 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_diff__divide__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  66 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom).  [assumption].
% 1.53/1.79  67 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,F),E) | E = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) | D = F # label(cls_vector__space_Oscale__right__imp__eq_0) # label(axiom).  [assumption].
% 1.53/1.79  68 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,F),E) | -c_RealVector_Ovector__space(C,B,A) | E = c_HOL_Ozero__class_Ozero(A) | D = F # label(cls_vector__space_Oscale__cancel__right_0) # label(axiom).  [assumption].
% 1.53/1.79  69 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,D),F) | D = c_HOL_Ozero__class_Ozero(B) | -c_RealVector_Ovector__space(C,B,A) | E = F # label(cls_vector__space_Oscale__left__imp__eq_0) # label(axiom).  [assumption].
% 1.53/1.79  70 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != hAPP(hAPP(C,D),F) | -c_RealVector_Ovector__space(C,B,A) | D = c_HOL_Ozero__class_Ozero(B) | E = F # label(cls_vector__space_Oscale__cancel__left_0) # label(axiom).  [assumption].
% 1.53/1.79  71 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),E) != c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(C,B,A) | E = c_HOL_Ozero__class_Ozero(A) | D = c_HOL_Ozero__class_Ozero(B) # label(cls_vector__space_Oscale__eq__0__iff_0) # label(axiom).  [assumption].
% 1.53/1.79  72 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom).  [assumption].
% 1.53/1.79  73 -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].
% 1.53/1.79  74 -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].
% 1.53/1.79  75 -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].
% 1.53/1.79  76 -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].
% 1.53/1.79  77 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(C,E),F)) = hAPP(hAPP(C,E),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__commute_0) # label(axiom).  [assumption].
% 1.53/1.79  78 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),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].
% 1.53/1.79  79 -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].
% 1.53/1.79  80 -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].
% 1.53/1.79  81 -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].
% 1.53/1.79  82 -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].
% 1.53/1.79  83 -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].
% 1.53/1.79  84 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(C,E),F)) = hAPP(hAPP(C,hAPP(c_HOL_Otimes__class_Otimes(D,B),E)),F) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__scale_0) # label(axiom).  [assumption].
% 1.53/1.79  85 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),D),E)),F) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(C,D),F)),hAPP(hAPP(C,E),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__diff__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  86 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(C,D),E)),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__right__diff__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  87 -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].
% 1.53/1.79  88 -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].
% 1.53/1.79  89 -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].
% 1.53/1.79  90 -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].
% 1.53/1.79  91 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(C,D),E)),hAPP(hAPP(C,D),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__right__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  92 -class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(B) | hAPP(hAPP(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(B),D),E)),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(C,D),F)),hAPP(hAPP(C,E),F)) | -c_RealVector_Ovector__space(C,B,A) # label(cls_vector__space_Oscale__left__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  93 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_add__divide__distrib_0) # label(axiom).  [assumption].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal).  [resolve(44,a,45,a)].
% 1.53/1.79  Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),A,tc_RealDef_Oreal).  [resolve(44,a,46,a)].
% 1.53/1.79  Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),A,tc_RealDef_Oreal) = B.  [resolve(44,a,47,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal).  [resolve(44,a,50,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal).  [resolve(44,a,51,a)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,52,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,53,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),C,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,54,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),C) = c_HOL_Ozero__class_Ozero(A).  [resolve(44,a,55,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,C),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A).  [resolve(44,a,56,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),C)),D) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(B,C),D)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,58,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),C) = hAPP(hAPP(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),D).  [resolve(44,a,60,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(c_HOL_Ouminus__class_Ouminus(A),D)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(B,C),D)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,61,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | hAPP(hAPP(B,C),c_HOL_Ozero__class_Ozero(A)) = hAPP(hAPP(B,D),c_HOL_Ozero__class_Ozero(A)).  [resolve(44,a,62,a)].
% 1.53/1.79  Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,63,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,64,a)].
% 1.53/1.79  Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)).  [resolve(44,a,65,a)].
% 1.53/1.79  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,66,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != hAPP(hAPP(B,E),D) | D = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | C = E.  [resolve(44,a,67,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != hAPP(hAPP(B,C),E) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | D = E.  [resolve(44,a,69,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | D = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,71,b)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal).  [resolve(44,a,72,a)].
% 1.53/1.79  Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,73,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,74,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A),A,tc_RealDef_Oreal).  [resolve(44,a,76,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(B,D),E)) = hAPP(hAPP(B,D),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,77,b)].
% 1.53/1.79  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,78,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | A = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,79,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B) = A | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,80,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,81,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,82,a)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C) = c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),B,tc_RealDef_Oreal).  [resolve(44,a,83,a)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(B,D),E)) = hAPP(hAPP(B,hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),E) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,84,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D)),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(B,C),E)),hAPP(hAPP(B,D),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,85,b)].
% 1.53/1.79  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,86,b)].
% 1.53/1.79  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(44,a,87,a)].
% 1.61/1.89  Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B).  [resolve(44,a,88,a)].
% 1.61/1.89  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) != hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,D,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal).  [resolve(44,a,89,a)].
% 1.61/1.89  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(44,a,90,a)].
% 1.61/1.89  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,91,b)].
% 1.61/1.89  Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(B,C),E)),hAPP(hAPP(B,D),E)) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A).  [resolve(44,a,92,b)].
% 1.61/1.89  Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)).  [resolve(44,a,93,a)].
% 1.61/1.89  94 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom).  [assumption].
% 1.61/1.89  95 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_Odiff_0) # label(axiom).  [assumption].
% 1.61/1.89  96 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR__minus__right_0) # label(axiom).  [assumption].
% 1.61/1.89  97 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__left__commute_0) # label(axiom).  [assumption].
% 1.61/1.89  98 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom).  [assumption].
% 1.61/1.89  99 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,E),D,E,A) # label(cls_scaleR__right_Osetsum_0) # label(axiom).  [assumption].
% 1.61/1.89  100 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),c_HOL_Ozero__class_Ozero(A)) # label(cls_scaleR__cancel__right_1) # label(axiom).  [assumption].
% 1.61/1.89  101 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),C) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom).  [assumption].
% 1.61/1.89  102 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_Oadd_0) # label(axiom).  [assumption].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)).  [resolve(94,a,95,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)).  [resolve(94,a,96,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)).  [resolve(94,a,97,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(94,a,98,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal).  [resolve(94,a,99,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(94,a,100,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C.  [resolve(94,a,101,a)].
% 1.61/1.92  Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)).  [resolve(94,a,102,a)].
% 1.61/1.92  103 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom).  [assumption].
% 1.61/1.92  104 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_Odiff__right_0) # label(axiom).  [assumption].
% 1.61/1.92  105 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR_Oadditive__right_0) # label(axiom).  [assumption].
% 1.61/1.92  106 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR_Ominus__right_0) # label(axiom).  [assumption].
% 1.61/1.92  107 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_OscaleR__right_0) # label(axiom).  [assumption].
% 1.61/1.92  108 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_OscaleR_0) # label(axiom).  [assumption].
% 1.69/1.95  109 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__right_0) # label(axiom).  [assumption].
% 1.69/1.95  110 -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR_Oadd__right_0) # label(axiom).  [assumption].
% 1.69/1.95  Derived: c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal).  [resolve(103,a,105,a)].
% 1.69/1.95  111 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 1.69/1.95  112 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_less__infI2_0) # label(axiom).  [assumption].
% 1.69/1.95  113 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_less__infI1_0) # label(axiom).  [assumption].
% 1.69/1.95  114 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),B)) # label(cls_inf__le1_0) # label(axiom).  [assumption].
% 1.69/1.95  115 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),C)) # label(cls_inf__le2_0) # label(axiom).  [assumption].
% 1.69/1.95  116 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__infI_0) # label(axiom).  [assumption].
% 1.69/1.95  117 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__inf__iff_2) # label(axiom).  [assumption].
% 1.69/1.95  118 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_inf__greatest_0) # label(axiom).  [assumption].
% 1.69/1.95  119 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom).  [assumption].
% 1.69/1.95  120 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom).  [assumption].
% 1.69/1.95  121 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom).  [assumption].
% 1.69/1.95  122 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom).  [assumption].
% 1.69/1.95  123 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__infI1_0) # label(axiom).  [assumption].
% 1.69/1.95  124 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_le__infI2_0) # label(axiom).  [assumption].
% 1.69/1.95  125 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom).  [assumption].
% 1.69/1.96  126 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom).  [assumption].
% 1.69/1.96  127 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_inf__absorb2_0) # label(axiom).  [assumption].
% 1.69/1.96  128 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__inf_1) # label(axiom).  [assumption].
% 1.69/1.96  129 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__inf_0) # label(axiom).  [assumption].
% 1.69/1.96  130 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom).  [assumption].
% 1.69/1.96  131 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom).  [assumption].
% 1.69/1.96  132 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom).  [assumption].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_fun(D,A)),E)).  [resolve(111,a,112,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(D,A)),E)).  [resolve(111,a,113,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),B)).  [resolve(111,a,114,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),C)).  [resolve(111,a,115,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)).  [resolve(111,a,116,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)).  [resolve(111,a,119,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)).  [resolve(111,a,120,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,A)))).  [resolve(111,a,121,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(C,A)))).  [resolve(111,a,122,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),E)).  [resolve(111,a,123,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),E)).  [resolve(111,a,124,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),B)).  [resolve(111,a,127,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)).  [resolve(111,a,128,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)).  [resolve(111,a,129,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)).  [resolve(111,a,130,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)).  [resolve(111,a,131,a)].
% 1.69/1.96  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B.  [resolve(111,a,132,a)].
% 1.69/1.96  133 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(133,a,112,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(133,a,113,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),A)).  [resolve(133,a,114,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),B)).  [resolve(133,a,115,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(133,a,116,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat).  [resolve(133,a,119,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat).  [resolve(133,a,120,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))).  [resolve(133,a,121,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat))).  [resolve(133,a,122,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(133,a,123,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(133,a,124,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(133,a,127,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(133,a,128,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(133,a,129,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat).  [resolve(133,a,130,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat).  [resolve(133,a,131,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A.  [resolve(133,a,132,a)].
% 1.69/1.96  134 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_bool),C)).  [resolve(134,a,112,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),C)).  [resolve(134,a,113,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),A)).  [resolve(134,a,114,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),B)).  [resolve(134,a,115,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(134,a,116,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool).  [resolve(134,a,119,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool).  [resolve(134,a,120,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))).  [resolve(134,a,121,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))).  [resolve(134,a,122,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)).  [resolve(134,a,123,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(B,tc_bool),C)).  [resolve(134,a,124,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)).  [resolve(134,a,127,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(134,a,128,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(134,a,129,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool).  [resolve(134,a,130,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool).  [resolve(134,a,131,a)].
% 1.69/1.96  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A.  [resolve(134,a,132,a)].
% 1.69/1.96  135 class_Lattices_Olower__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)).  [resolve(135,a,112,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(135,a,113,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(135,a,114,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(135,a,115,a)].
% 1.69/1.96  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(135,a,116,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(135,a,119,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(135,a,120,a)].
% 1.74/1.99  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal))).  [resolve(135,a,121,a)].
% 1.74/1.99  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_RealDef_Oreal))).  [resolve(135,a,122,a)].
% 1.74/1.99  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(135,a,123,a)].
% 1.74/1.99  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)).  [resolve(135,a,124,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = B | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)).  [resolve(135,a,127,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) != A | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(135,a,128,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = A | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(135,a,129,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_RealDef_Oreal).  [resolve(135,a,130,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal).  [resolve(135,a,131,a)].
% 1.74/1.99  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_RealDef_Oreal) = A.  [resolve(135,a,132,a)].
% 1.74/1.99  136 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom).  [assumption].
% 1.74/1.99  137 -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].
% 1.74/1.99  138 -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(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom).  [assumption].
% 1.74/1.99  139 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),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].
% 1.74/1.99  140 -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(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__self__iff_0) # label(axiom).  [assumption].
% 1.74/1.99  141 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__minus__self__iff_1) # label(axiom).  [assumption].
% 1.74/1.99  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | B = A.  [resolve(136,a,137,a)].
% 1.74/1.99  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(136,a,140,a)].
% 1.74/2.03  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(136,a,141,a)].
% 1.74/2.03  142 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom).  [assumption].
% 1.74/2.03  143 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom).  [assumption].
% 1.74/2.03  144 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom).  [assumption].
% 1.74/2.03  145 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I30_J_0) # label(axiom).  [assumption].
% 1.74/2.03  146 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Ozero__class_Ozero(A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_group__add__class_Odiff__0_0) # label(axiom).  [assumption].
% 1.74/2.03  147 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__minus_0) # label(axiom).  [assumption].
% 1.74/2.03  148 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I34_J_0) # label(axiom).  [assumption].
% 1.74/2.03  149 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom).  [assumption].
% 1.74/2.03  150 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom).  [assumption].
% 1.74/2.03  151 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom).  [assumption].
% 1.74/2.03  152 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom).  [assumption].
% 1.74/2.03  153 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom).  [assumption].
% 1.74/2.03  154 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom).  [assumption].
% 1.74/2.03  155 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom).  [assumption].
% 1.74/2.03  156 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom).  [assumption].
% 1.74/2.03  157 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) = C # label(cls_minus__unique_0) # label(axiom).  [assumption].
% 1.74/2.03  158 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom).  [assumption].
% 1.74/2.03  159 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) # label(cls_neg__0__equal__iff__equal_1) # label(axiom).  [assumption].
% 1.74/2.03  160 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) # label(cls_diff__minus__eq__add_0) # label(axiom).  [assumption].
% 1.74/2.03  161 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__equation__iff_1) # label(axiom).  [assumption].
% 1.74/2.03  162 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_1) # label(axiom).  [assumption].
% 1.74/2.03  163 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_0) # label(axiom).  [assumption].
% 1.74/2.03  164 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__minus_0) # label(axiom).  [assumption].
% 1.74/2.03  165 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10) # label(cls_pordered__ring_Oring__simps_I36_J_0) # label(axiom).  [assumption].
% 1.74/2.03  166 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_minus__add_0) # label(axiom).  [assumption].
% 1.74/2.03  167 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom).  [assumption].
% 1.74/2.03  168 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom).  [assumption].
% 1.74/2.03  169 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom).  [assumption].
% 1.74/2.03  170 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom).  [assumption].
% 1.74/2.03  171 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom).  [assumption].
% 1.74/2.03  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B.  [resolve(142,a,143,a)].
% 1.74/2.03  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(142,a,144,a)].
% 1.74/2.03  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7).  [resolve(142,a,145,a)].
% 1.74/2.03  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A).  [resolve(142,a,146,a)].
% 1.74/2.03  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)).  [resolve(142,a,147,a)].
% 1.74/2.03  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10).  [resolve(142,a,148,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(142,a,149,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A.  [resolve(142,a,150,a)].
% 1.83/2.06  Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A.  [resolve(142,a,152,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(142,a,153,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(142,a,154,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B.  [resolve(142,a,156,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) = B.  [resolve(142,a,157,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B).  [resolve(142,a,158,a)].
% 1.83/2.06  Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(142,a,159,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B).  [resolve(142,a,160,a)].
% 1.83/2.06  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = A.  [resolve(142,a,161,a)].
% 1.83/2.06  Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)).  [resolve(142,a,162,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) | -c_Ring__and__Field_Opordered__ring(C,D,E,F,V6,V7,V8,V9).  [resolve(142,a,165,a)].
% 1.83/2.06  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)).  [resolve(142,a,166,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = B.  [resolve(142,a,167,a)].
% 1.83/2.06  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(142,a,168,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)),B)) = B.  [resolve(142,a,169,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B)),B) = A.  [resolve(142,a,170,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),B) = A.  [resolve(142,a,171,a)].
% 1.83/2.06  172 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom).  [assumption].
% 1.83/2.06  173 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__le__0__iff__le_0) # label(axiom).  [assumption].
% 1.83/2.06  174 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__le__0__iff__le_1) # label(axiom).  [assumption].
% 1.83/2.06  175 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I27_J_1) # label(axiom).  [assumption].
% 1.83/2.06  176 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I27_J_0) # label(axiom).  [assumption].
% 1.83/2.06  177 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I28_J_1) # label(axiom).  [assumption].
% 1.83/2.06  178 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I28_J_0) # label(axiom).  [assumption].
% 1.83/2.06  179 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | 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].
% 1.83/2.06  180 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | 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].
% 1.83/2.06  181 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom).  [assumption].
% 1.83/2.06  182 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom).  [assumption].
% 1.83/2.06  183 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I26_J_0) # label(axiom).  [assumption].
% 1.83/2.06  184 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I26_J_1) # label(axiom).  [assumption].
% 1.83/2.06  185 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I25_J_0) # label(axiom).  [assumption].
% 1.83/2.06  186 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I25_J_1) # label(axiom).  [assumption].
% 1.83/2.06  187 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_neg__less__iff__less_1) # label(axiom).  [assumption].
% 1.83/2.06  188 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__less__iff__less_0) # label(axiom).  [assumption].
% 1.83/2.06  189 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__le__iff__le_0) # label(axiom).  [assumption].
% 1.83/2.06  190 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__imp__neg__le_0) # label(axiom).  [assumption].
% 1.83/2.06  191 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__less__0__iff__less_1) # label(axiom).  [assumption].
% 1.83/2.06  192 -class_OrderedGroup_Opordered__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(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__less__0__iff__less_0) # label(axiom).  [assumption].
% 1.83/2.06  193 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__0__le__iff__le_0) # label(axiom).  [assumption].
% 1.83/2.06  194 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__0__le__iff__le_1) # label(axiom).  [assumption].
% 1.83/2.06  195 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I23_J_1) # label(axiom).  [assumption].
% 1.83/2.06  196 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I23_J_0) # label(axiom).  [assumption].
% 1.83/2.06  197 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I24_J_1) # label(axiom).  [assumption].
% 1.83/2.06  198 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I24_J_0) # label(axiom).  [assumption].
% 1.83/2.06  199 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),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].
% 1.83/2.06  200 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom).  [assumption].
% 1.83/2.06  201 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I20_J_0) # label(axiom).  [assumption].
% 1.83/2.06  202 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I20_J_1) # label(axiom).  [assumption].
% 1.83/2.06  203 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I19_J_0) # label(axiom).  [assumption].
% 1.83/2.06  204 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I19_J_1) # label(axiom).  [assumption].
% 1.83/2.06  205 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),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].
% 1.83/2.06  206 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom).  [assumption].
% 1.83/2.06  207 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_1) # label(axiom).  [assumption].
% 1.83/2.06  208 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_0) # label(axiom).  [assumption].
% 1.83/2.06  209 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_1) # label(axiom).  [assumption].
% 1.83/2.06  210 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_0) # label(axiom).  [assumption].
% 1.83/2.06  211 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__less__iff_1) # label(axiom).  [assumption].
% 1.83/2.06  212 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__less__iff_0) # label(axiom).  [assumption].
% 1.83/2.06  213 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__iff_1) # label(axiom).  [assumption].
% 1.83/2.06  214 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__minus__iff_0) # label(axiom).  [assumption].
% 1.83/2.06  215 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__le__iff_1) # label(axiom).  [assumption].
% 1.83/2.06  216 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A),B)) # label(cls_minus__le__iff_0) # label(axiom).  [assumption].
% 1.83/2.06  217 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__iff_1) # label(axiom).  [assumption].
% 1.83/2.06  218 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_le__minus__iff_0) # label(axiom).  [assumption].
% 1.83/2.06  219 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E))) # label(cls_le__add__right__mono_0) # label(axiom).  [assumption].
% 1.83/2.06  220 -class_OrderedGroup_Opordered__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_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_neg__0__less__iff__less_0) # label(axiom).  [assumption].
% 1.83/2.06  221 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_neg__0__less__iff__less_1) # label(axiom).  [assumption].
% 1.83/2.06  222 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_0) # label(axiom).  [assumption].
% 1.83/2.06  223 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_1) # label(axiom).  [assumption].
% 1.83/2.06  224 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C))) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_0) # label(axiom).  [assumption].
% 1.83/2.06  225 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_1) # label(axiom).  [assumption].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,173,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(172,a,174,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,175,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,176,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,177,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,178,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),D)).  [resolve(172,a,179,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)).  [resolve(172,a,180,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)).  [resolve(172,a,181,a)].
% 1.83/2.06  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),D) | hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)).  [resolve(172,a,182,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,183,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,184,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,185,a)].
% 1.83/2.06  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10).  [resolve(172,a,186,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)).  [resolve(172,a,187,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,188,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,189,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)).  [resolve(172,a,190,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(172,a,191,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,192,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,193,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,194,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,195,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,196,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,197,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,198,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(172,a,199,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,200,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,201,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,202,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,203,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,204,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)).  [resolve(172,a,205,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,206,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,207,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,208,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,209,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(172,a,210,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)).  [resolve(172,a,211,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,213,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)).  [resolve(172,a,215,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,217,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D))).  [resolve(172,a,219,a)].
% 1.83/2.07  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))).  [resolve(172,a,220,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(172,a,221,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,222,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,223,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),C),B))) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,224,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(172,a,225,a)].
% 1.83/2.10  226 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom).  [assumption].
% 1.83/2.10  227 -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].
% 1.83/2.10  228 -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].
% 1.83/2.10  229 -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].
% 1.83/2.10  230 -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].
% 1.83/2.10  231 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom).  [assumption].
% 1.83/2.10  232 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom).  [assumption].
% 1.83/2.10  233 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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__le__zero__iff_2) # label(axiom).  [assumption].
% 1.83/2.10  234 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom).  [assumption].
% 1.83/2.10  235 -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].
% 1.83/2.10  236 -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].
% 1.83/2.10  237 -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].
% 1.83/2.10  238 -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].
% 1.83/2.10  239 -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].
% 1.83/2.10  240 -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].
% 1.83/2.10  241 -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].
% 1.83/2.10  242 -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].
% 1.83/2.10  243 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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))))) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom).  [assumption].
% 1.83/2.10  244 -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].
% 1.83/2.10  245 -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].
% 1.83/2.10  246 -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].
% 1.83/2.10  247 -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].
% 1.83/2.10  248 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) # label(cls_sum__squares__ge__zero_0) # label(axiom).  [assumption].
% 1.83/2.10  249 -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].
% 1.83/2.10  250 -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].
% 1.83/2.10  251 -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].
% 1.83/2.10  252 -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].
% 1.83/2.10  253 -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].
% 1.83/2.10  254 -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].
% 1.83/2.10  255 -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].
% 1.83/2.10  256 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom).  [assumption].
% 1.83/2.10  257 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom).  [assumption].
% 1.83/2.10  258 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom).  [assumption].
% 1.83/2.10  259 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B)),hAPP(c_HOL_Otimes__class_Otimes(C,A),C)))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom).  [assumption].
% 1.83/2.10  260 -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].
% 1.83/2.10  261 -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].
% 1.83/2.10  262 -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].
% 1.83/2.10  263 -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].
% 1.83/2.10  264 -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].
% 1.83/2.10  265 -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].
% 1.83/2.10  266 -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].
% 1.83/2.10  267 -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].
% 1.83/2.10  268 -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].
% 1.83/2.10  269 -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].
% 1.83/2.10  270 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),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))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom).  [assumption].
% 1.83/2.10  271 -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].
% 1.83/2.10  272 -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].
% 1.83/2.10  273 -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].
% 1.83/2.10  274 -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].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,227,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,228,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,229,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,230,a)].
% 1.83/2.10  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(226,a,231,a)].
% 1.83/2.10  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(226,a,232,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,233,a)].
% 1.83/2.10  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,234,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,235,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A))).  [resolve(226,a,236,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(226,a,237,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,238,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))).  [resolve(226,a,239,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))).  [resolve(226,a,240,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))).  [resolve(226,a,241,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))).  [resolve(226,a,242,a)].
% 1.83/2.10  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))))).  [resolve(226,a,243,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))).  [resolve(226,a,244,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))).  [resolve(226,a,245,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))).  [resolve(226,a,246,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))).  [resolve(226,a,247,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))).  [resolve(226,a,248,a)].
% 1.83/2.10  Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,249,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(226,a,250,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,251,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(226,a,252,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(226,a,253,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,254,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,255,a)].
% 1.83/2.10  Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,256,a)].
% 1.83/2.10  Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,257,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(226,a,258,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B)))) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(226,a,259,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,260,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(226,a,261,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,263,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(226,a,264,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(226,a,267,a)].
% 1.83/2.10  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(226,a,269,a)].
% 1.83/2.10  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(226,a,270,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))).  [resolve(226,a,271,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))).  [resolve(226,a,272,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))).  [resolve(226,a,273,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A))).  [resolve(226,a,274,a)].
% 1.88/2.14  275 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom).  [assumption].
% 1.88/2.14  276 -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].
% 1.88/2.14  277 -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].
% 1.88/2.14  278 -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].
% 1.88/2.14  279 -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].
% 1.88/2.14  280 -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].
% 1.88/2.14  281 -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].
% 1.88/2.14  282 -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].
% 1.88/2.14  283 -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].
% 1.88/2.14  284 -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].
% 1.88/2.14  285 -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].
% 1.88/2.14  286 -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].
% 1.88/2.14  287 -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].
% 1.88/2.14  288 -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].
% 1.88/2.14  289 -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].
% 1.88/2.14  290 -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].
% 1.88/2.14  291 -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].
% 1.88/2.14  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(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(275,a,276,a)].
% 1.88/2.14  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(275,a,277,a)].
% 1.88/2.14  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(275,a,279,a)].
% 1.88/2.14  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(275,a,280,a)].
% 1.88/2.14  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(275,a,281,a)].
% 1.88/2.14  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(275,a,282,a)].
% 1.88/2.14  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(275,a,283,a)].
% 1.88/2.14  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(275,a,284,a)].
% 1.88/2.14  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(275,a,285,a)].
% 1.88/2.14  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(275,a,286,a)].
% 1.88/2.14  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(275,a,287,a)].
% 1.88/2.14  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(275,a,288,a)].
% 1.88/2.14  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(275,a,289,a)].
% 1.88/2.14  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(275,a,290,a)].
% 1.88/2.14  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(275,a,291,a)].
% 1.88/2.14  292 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom).  [assumption].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(292,a,276,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(292,a,277,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(292,a,279,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))).  [resolve(292,a,280,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A))).  [resolve(292,a,281,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(292,a,282,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))).  [resolve(292,a,283,a)].
% 1.88/2.14  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(292,a,284,a)].
% 1.93/2.23  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(292,a,285,a)].
% 1.93/2.23  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))).  [resolve(292,a,286,a)].
% 1.93/2.23  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(292,a,288,a)].
% 1.93/2.23  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(292,a,291,a)].
% 1.93/2.23  293 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom).  [assumption].
% 1.93/2.23  294 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -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].
% 1.93/2.23  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -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(293,a,294,a)].
% 1.93/2.23  295 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom).  [assumption].
% 1.93/2.23  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(295,a,294,a)].
% 1.93/2.23  296 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom).  [assumption].
% 1.93/2.23  297 -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].
% 1.93/2.23  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(296,a,297,a)].
% 1.93/2.23  298 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom).  [assumption].
% 1.93/2.23  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)).  [resolve(298,a,297,a)].
% 2.01/2.29  299 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom).  [assumption].
% 2.01/2.29  300 -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].
% 2.01/2.29  301 -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].
% 2.01/2.29  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(299,a,301,a)].
% 2.01/2.29  302 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom).  [assumption].
% 2.01/2.29  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(302,a,301,a)].
% 2.01/2.29  303 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom).  [assumption].
% 2.01/2.29  304 -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].
% 2.01/2.29  305 -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].
% 2.01/2.29  306 -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].
% 2.01/2.29  307 -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].
% 2.01/2.29  308 -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].
% 2.01/2.29  309 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_lessequals(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F))) # label(cls_le__add__iff2_1) # label(axiom).  [assumption].
% 2.01/2.29  310 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A),E)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)),F))) # label(cls_le__add__iff2_0) # label(axiom).  [assumption].
% 2.01/2.29  311 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D),A),F)) # label(cls_le__add__iff1_1) # label(axiom).  [assumption].
% 2.01/2.29  312 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)),E),A),F)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),F))) # label(cls_le__add__iff1_0) # label(axiom).  [assumption].
% 2.01/2.29  313 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)),E),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),F))) # label(cls_less__add__iff1_0) # label(axiom).  [assumption].
% 2.01/2.29  314 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E),A),C)),D),A),F)) # label(cls_less__add__iff1_1) # label(axiom).  [assumption].
% 2.01/2.29  315 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A),E)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)),F))) # label(cls_less__add__iff2_0) # label(axiom).  [assumption].
% 2.01/2.29  316 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(E,A),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),A),C)),F))) # label(cls_less__add__iff2_1) # label(axiom).  [assumption].
% 2.01/2.29  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)).  [resolve(303,a,304,a)].
% 2.01/2.29  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),A)).  [resolve(303,a,305,a)].
% 2.01/2.29  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E))).  [resolve(303,a,309,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal),D)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)),E))).  [resolve(303,a,310,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),E)).  [resolve(303,a,311,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),E)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)),E))).  [resolve(303,a,312,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),D),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)),E))).  [resolve(303,a,313,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),D),tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),E)).  [resolve(303,a,314,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal),D)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)),E))).  [resolve(303,a,315,a)].
% 2.06/2.32  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(D,tc_RealDef_Oreal),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),D),A),tc_RealDef_Oreal),B)),E))).  [resolve(303,a,316,a)].
% 2.06/2.32  317 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom).  [assumption].
% 2.06/2.32  318 -class_RealVector_Oreal__normed__algebra(A) | c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(B,A),A,A) # label(cls_mult_Oadditive__right_0) # label(axiom).  [assumption].
% 2.06/2.32  319 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__left_0) # label(axiom).  [assumption].
% 2.06/2.32  320 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__left_Ominus_0) # label(axiom).  [assumption].
% 2.06/2.32  321 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__right_0) # label(axiom).  [assumption].
% 2.06/2.32  322 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__right_Ominus_0) # label(axiom).  [assumption].
% 2.06/2.32  323 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_mult__right_Osetsum_0) # label(axiom).  [assumption].
% 2.06/2.32  324 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_OscaleR__left_0) # label(axiom).  [assumption].
% 2.06/2.32  325 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_OscaleR_0) # label(axiom).  [assumption].
% 2.06/2.32  326 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_OscaleR__right_0) # label(axiom).  [assumption].
% 2.06/2.32  327 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_OscaleR_0) # label(axiom).  [assumption].
% 2.06/2.32  328 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),A),E))),hAPP(c_HOL_Otimes__class_Otimes(D,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom).  [assumption].
% 2.06/2.32  329 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_Odiff_0) # label(axiom).  [assumption].
% 2.06/2.32  330 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_Odiff__right_0) # label(axiom).  [assumption].
% 2.06/2.32  331 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_Odiff__left_0) # label(axiom).  [assumption].
% 2.06/2.32  332 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_Odiff_0) # label(axiom).  [assumption].
% 2.06/2.32  333 -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].
% 2.06/2.32  334 -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].
% 2.06/2.32  335 -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].
% 2.06/2.32  336 -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].
% 2.06/2.32  337 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_Oadd__left_0) # label(axiom).  [assumption].
% 2.06/2.32  338 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_Oadd_0) # label(axiom).  [assumption].
% 2.06/2.32  339 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_Oadd__right_0) # label(axiom).  [assumption].
% 2.06/2.32  340 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_Oadd_0) # label(axiom).  [assumption].
% 2.06/2.32  Derived: c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal).  [resolve(317,a,318,a)].
% 2.06/2.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)).  [resolve(317,a,319,a)].
% 2.06/2.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)).  [resolve(317,a,321,a)].
% 2.06/2.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal).  [resolve(317,a,323,a)].
% 2.06/2.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)).  [resolve(317,a,324,a)].
% 2.06/2.32  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)).  [resolve(317,a,326,a)].
% 2.11/2.35  Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D))),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),D))),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D))).  [resolve(317,a,328,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)).  [resolve(317,a,329,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)).  [resolve(317,a,331,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(317,a,333,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(317,a,335,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)).  [resolve(317,a,337,a)].
% 2.11/2.35  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)).  [resolve(317,a,339,a)].
% 2.11/2.35  341 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom).  [assumption].
% 2.11/2.35  342 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom).  [assumption].
% 2.11/2.35  343 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),B) # label(cls_square__eq__iff_1) # label(axiom).  [assumption].
% 2.11/2.35  344 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom).  [assumption].
% 2.11/2.35  345 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),B) != hAPP(c_HOL_Otimes__class_Otimes(C,A),C) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_square__eq__iff_0) # label(axiom).  [assumption].
% 2.11/2.35  346 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom).  [assumption].
% 2.11/2.35  347 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom).  [assumption].
% 2.11/2.38  348 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),E)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom).  [assumption].
% 2.11/2.38  349 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom).  [assumption].
% 2.11/2.38  350 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom).  [assumption].
% 2.11/2.38  351 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom).  [assumption].
% 2.11/2.38  352 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom).  [assumption].
% 2.11/2.38  353 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom).  [assumption].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(341,a,342,a)].
% 2.11/2.38  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A) != hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B.  [resolve(341,a,345,a)].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)) | B = D | A = C.  [resolve(341,a,347,a)].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(341,a,349,a)].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)).  [resolve(341,a,350,a)].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).  [resolve(341,a,352,a)].
% 2.11/2.38  Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C.  [resolve(341,a,353,a)].
% 2.11/2.38  354 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom).  [assumption].
% 2.11/2.38  355 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,D,A),A),C)) # label(cls_divide__less__eq_0) # label(axiom).  [assumption].
% 2.11/2.38  356 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_6) # label(axiom).  [assumption].
% 2.11/2.38  357 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -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_Oinverse__class_Odivide(D,C,A))) # label(cls_less__divide__eq_0) # label(axiom).  [assumption].
% 2.11/2.38  358 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -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(B,A),D),A),C)) # label(cls_less__divide__eq_6) # label(axiom).  [assumption].
% 2.11/2.38  359 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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),C)) # label(cls_mult__imp__div__pos__less_0) # label(axiom).  [assumption].
% 2.11/2.38  360 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__imp__less__div__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  361 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__less__divide__iff_0) # label(axiom).  [assumption].
% 2.11/2.38  362 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__less__divide__iff_1) # label(axiom).  [assumption].
% 2.11/2.38  363 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__less__divide__iff_2) # label(axiom).  [assumption].
% 2.11/2.38  364 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__less__divide__iff_3) # label(axiom).  [assumption].
% 2.11/2.38  365 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(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(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__nonneg__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  366 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),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_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__nonpos__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  367 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_divide__right__mono_0) # label(axiom).  [assumption].
% 2.11/2.38  368 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_divide__right__mono__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  369 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_8) # label(axiom).  [assumption].
% 2.11/2.38  370 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_8) # label(axiom).  [assumption].
% 2.11/2.38  371 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_lessequals(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__less_0) # label(axiom).  [assumption].
% 2.11/2.38  372 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | 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),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__less__eq_2) # label(axiom).  [assumption].
% 2.11/2.38  373 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | 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),C)) # label(cls_divide__less__eq_3) # label(axiom).  [assumption].
% 2.11/2.38  374 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_8) # label(axiom).  [assumption].
% 2.11/2.38  375 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -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),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_9) # label(axiom).  [assumption].
% 2.11/2.38  376 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),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_Oinverse__class_Odivide(D,C,A))) # label(cls_less__divide__eq_2) # label(axiom).  [assumption].
% 2.11/2.38  377 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -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_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_less__divide__eq_3) # label(axiom).  [assumption].
% 2.11/2.38  378 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_8) # label(axiom).  [assumption].
% 2.11/2.38  379 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,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),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_9) # label(axiom).  [assumption].
% 2.11/2.38  380 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,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_divide__neg__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  381 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(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_divide__pos__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  382 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(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_zero__less__divide__iff_4) # label(axiom).  [assumption].
% 2.11/2.38  383 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,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_zero__less__divide__iff_5) # label(axiom).  [assumption].
% 2.11/2.38  384 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,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),D)) # label(cls_divide__strict__right__mono_0) # label(axiom).  [assumption].
% 2.11/2.38  385 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,C,A))) | -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_divide__strict__right__mono__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  386 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(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_divide__nonneg__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  387 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,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_divide__nonpos__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  388 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__imp__le__div__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  389 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(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),C)) # label(cls_mult__imp__div__pos__le_0) # label(axiom).  [assumption].
% 2.11/2.38  390 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -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),C)) # label(cls_le__divide__eq_6) # label(axiom).  [assumption].
% 2.11/2.38  391 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_le__divide__eq_0) # label(axiom).  [assumption].
% 2.11/2.38  392 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_6) # label(axiom).  [assumption].
% 2.11/2.38  393 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,D,A),A),C)) # label(cls_divide__le__eq_0) # label(axiom).  [assumption].
% 2.11/2.38  394 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),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_divide__le__0__iff_5) # label(axiom).  [assumption].
% 2.11/2.38  395 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(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(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__le__0__iff_4) # label(axiom).  [assumption].
% 2.11/2.38  396 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_divide__left__mono__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  397 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_divide__left__mono_0) # label(axiom).  [assumption].
% 2.11/2.38  398 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__less2_0) # label(axiom).  [assumption].
% 2.11/2.38  399 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__le__eq_5) # label(axiom).  [assumption].
% 2.11/2.38  400 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_7) # label(axiom).  [assumption].
% 2.11/2.38  401 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(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),D)) # label(cls_le__divide__eq_5) # label(axiom).  [assumption].
% 2.11/2.38  402 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_7) # label(axiom).  [assumption].
% 2.11/2.38  403 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_0) # label(axiom).  [assumption].
% 2.11/2.38  404 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_1) # label(axiom).  [assumption].
% 2.11/2.38  405 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_2) # label(axiom).  [assumption].
% 2.11/2.38  406 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__le__0__iff_3) # label(axiom).  [assumption].
% 2.11/2.38  407 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__le__divide__iff_3) # label(axiom).  [assumption].
% 2.11/2.38  408 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__le__divide__iff_2) # label(axiom).  [assumption].
% 2.11/2.38  409 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(C,B,A))) # label(cls_zero__le__divide__iff_1) # label(axiom).  [assumption].
% 2.11/2.38  410 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(B,C,A))) # label(cls_zero__le__divide__iff_0) # label(axiom).  [assumption].
% 2.11/2.38  411 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -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),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__less__eq_1) # label(axiom).  [assumption].
% 2.11/2.38  412 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__less__eq_4) # label(axiom).  [assumption].
% 2.11/2.38  413 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -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),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__less__eq_5) # label(axiom).  [assumption].
% 2.11/2.38  414 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__less__eq_7) # label(axiom).  [assumption].
% 2.11/2.38  415 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Oinverse__class_Odivide(B,D,A))) # label(cls_less__divide__eq_1) # label(axiom).  [assumption].
% 2.11/2.38  416 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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),D)) # label(cls_less__divide__eq_4) # label(axiom).  [assumption].
% 2.11/2.38  417 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,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),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_less__divide__eq_5) # label(axiom).  [assumption].
% 2.11/2.38  418 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -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_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_less__divide__eq_7) # label(axiom).  [assumption].
% 2.11/2.38  419 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(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_zero__le__divide__iff_4) # label(axiom).  [assumption].
% 2.11/2.38  420 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oinverse__class_Odivide(B,C,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_zero__le__divide__iff_5) # label(axiom).  [assumption].
% 2.11/2.38  421 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(D,E,A))) | -hBOOL(hAPP(c_lessequals(E,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_frac__le_0) # label(axiom).  [assumption].
% 2.11/2.38  422 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_divide__strict__left__mono_0) # label(axiom).  [assumption].
% 2.11/2.38  423 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Oinverse__class_Odivide(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -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)) # label(cls_divide__strict__left__mono__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  424 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_3) # label(axiom).  [assumption].
% 2.11/2.38  425 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_2) # label(axiom).  [assumption].
% 2.11/2.38  426 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_1) # label(axiom).  [assumption].
% 2.11/2.38  427 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_divide__less__0__iff_0) # label(axiom).  [assumption].
% 2.11/2.38  428 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C)) # label(cls_le__divide__eq_9) # label(axiom).  [assumption].
% 2.11/2.38  429 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_le__divide__eq_3) # label(axiom).  [assumption].
% 2.11/2.38  430 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,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),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(D,C,A))) # label(cls_le__divide__eq_2) # label(axiom).  [assumption].
% 2.11/2.38  431 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C))) # label(cls_divide__le__eq_9) # label(axiom).  [assumption].
% 2.11/2.38  432 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | 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),C)) # label(cls_divide__le__eq_3) # label(axiom).  [assumption].
% 2.11/2.38  433 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | 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),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__le__eq_2) # label(axiom).  [assumption].
% 2.11/2.38  434 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D)) | -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),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),A),B)) # label(cls_divide__le__eq_1) # label(axiom).  [assumption].
% 2.11/2.38  435 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_divide__le__eq_4) # label(axiom).  [assumption].
% 2.11/2.38  436 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oinverse__class_Odivide(B,D,A))) # label(cls_le__divide__eq_1) # label(axiom).  [assumption].
% 2.11/2.38  437 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oinverse__class_Odivide(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(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),D)) # label(cls_le__divide__eq_4) # label(axiom).  [assumption].
% 2.11/2.38  438 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),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_divide__neg__pos_0) # label(axiom).  [assumption].
% 2.11/2.38  439 -class_Ring__and__Field_Oordered__field(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__pos__neg_0) # label(axiom).  [assumption].
% 2.11/2.38  440 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(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(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_divide__less__0__iff_4) # label(axiom).  [assumption].
% 2.11/2.38  441 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),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_divide__less__0__iff_5) # label(axiom).  [assumption].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,355,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,356,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))).  [resolve(354,a,357,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,358,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,359,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,360,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))).  [resolve(354,a,361,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))).  [resolve(354,a,362,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))).  [resolve(354,a,363,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))).  [resolve(354,a,364,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,365,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,366,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(354,a,367,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),A)).  [resolve(354,a,368,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,369,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,370,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,371,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,372,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,373,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,374,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,375,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))).  [resolve(354,a,376,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,377,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,378,a)].
% 2.11/2.38  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,379,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,380,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,381,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(354,a,384,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),A)).  [resolve(354,a,385,a)].
% 2.11/2.38  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,386,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,387,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,388,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,389,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))).  [resolve(354,a,391,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,393,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,394,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,395,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)).  [resolve(354,a,396,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(C,tc_RealDef_Oreal),B)).  [resolve(354,a,397,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,398,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,399,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,400,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,401,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,402,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,403,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,404,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,405,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,406,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))).  [resolve(354,a,407,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))).  [resolve(354,a,408,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal))).  [resolve(354,a,409,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))).  [resolve(354,a,410,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,411,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,412,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,413,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,414,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))).  [resolve(354,a,415,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,416,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,417,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,418,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,419,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,420,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(D,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,421,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),B)).  [resolve(354,a,422,a)].
% 2.11/2.39  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)).  [resolve(354,a,423,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,424,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,425,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,426,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,427,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B)).  [resolve(354,a,428,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,429,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal))).  [resolve(354,a,430,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B))).  [resolve(354,a,431,a)].
% 2.11/2.39  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,432,a)].
% 2.16/2.42  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,433,a)].
% 2.16/2.42  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,434,a)].
% 2.16/2.42  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(354,a,435,a)].
% 2.16/2.42  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal))).  [resolve(354,a,436,a)].
% 2.16/2.42  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(354,a,437,a)].
% 2.16/2.42  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(354,a,438,a)].
% 2.16/2.42  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(354,a,439,a)].
% 2.16/2.42  442 class_OrderedGroup_Osemigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__mult) # label(axiom).  [assumption].
% 2.16/2.42  443 -class_OrderedGroup_Osemigroup__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)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I33_J_0) # label(axiom).  [assumption].
% 2.16/2.42  444 -class_OrderedGroup_Osemigroup__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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I37_J_0) # label(axiom).  [assumption].
% 2.16/2.44  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)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(442,a,443,a)].
% 2.16/2.44  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)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(442,a,444,a)].
% 2.16/2.44  445 class_OrderedGroup_Osemigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__mult) # label(axiom).  [assumption].
% 2.16/2.44  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(445,a,443,a)].
% 2.16/2.44  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(445,a,444,a)].
% 2.16/2.44  446 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom).  [assumption].
% 2.16/2.44  447 -class_OrderedGroup_Oab__semigroup__mult(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)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I31_J_0) # label(axiom).  [assumption].
% 2.16/2.44  448 -class_OrderedGroup_Oab__semigroup__mult(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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I35_J_0) # label(axiom).  [assumption].
% 2.16/2.44  449 -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].
% 2.16/2.44  450 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I32_J_0) # label(axiom).  [assumption].
% 2.16/2.44  451 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I36_J_0) # label(axiom).  [assumption].
% 2.16/2.44  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)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(446,a,447,a)].
% 2.16/2.44  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)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(446,a,448,a)].
% 2.16/2.44  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(446,a,449,a)].
% 2.16/2.44  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7).  [resolve(446,a,450,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10).  [resolve(446,a,451,a)].
% 2.21/2.47  452 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom).  [assumption].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(452,a,447,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(452,a,448,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)).  [resolve(452,a,449,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7).  [resolve(452,a,450,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10).  [resolve(452,a,451,a)].
% 2.21/2.47  453 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom).  [assumption].
% 2.21/2.47  454 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I18_J_0) # label(axiom).  [assumption].
% 2.21/2.47  455 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I17_J_0) # label(axiom).  [assumption].
% 2.21/2.47  456 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I21_J_0) # label(axiom).  [assumption].
% 2.21/2.47  457 -class_Ring__and__Field_Osemiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I22_J_0) # label(axiom).  [assumption].
% 2.21/2.47  458 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C)),E) # label(cls_combine__common__factor_0) # label(axiom).  [assumption].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(453,a,454,a)].
% 2.21/2.47  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8).  [resolve(453,a,455,a)].
% 2.21/2.50  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(453,a,456,a)].
% 2.21/2.50  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(453,a,457,a)].
% 2.21/2.50  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),B)),D).  [resolve(453,a,458,a)].
% 2.21/2.50  459 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom).  [assumption].
% 2.21/2.50  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B)),D).  [resolve(459,a,458,a)].
% 2.21/2.50  460 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 2.21/2.50  461 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__supE_0) # label(axiom).  [assumption].
% 2.21/2.50  462 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__supE_1) # label(axiom).  [assumption].
% 2.21/2.50  463 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__supI1_0) # label(axiom).  [assumption].
% 2.21/2.50  464 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI2_0) # label(axiom).  [assumption].
% 2.21/2.50  465 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__sup__iff_0) # label(axiom).  [assumption].
% 2.21/2.50  466 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__sup__iff_1) # label(axiom).  [assumption].
% 2.21/2.50  467 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__supI1_0) # label(axiom).  [assumption].
% 2.21/2.50  468 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_less__supI2_0) # label(axiom).  [assumption].
% 2.21/2.50  469 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI_0) # label(axiom).  [assumption].
% 2.21/2.50  470 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A))) # label(cls_sup__ge1_0) # label(axiom).  [assumption].
% 2.21/2.50  471 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,B,A))) # label(cls_sup__ge2_0) # label(axiom).  [assumption].
% 2.21/2.50  472 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_sup__least_0) # label(axiom).  [assumption].
% 2.21/2.50  473 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__sup__iff_2) # label(axiom).  [assumption].
% 2.21/2.50  474 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom).  [assumption].
% 2.21/2.50  475 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom).  [assumption].
% 2.21/2.50  476 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom).  [assumption].
% 2.21/2.50  477 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_0) # label(axiom).  [assumption].
% 2.21/2.50  478 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_1) # label(axiom).  [assumption].
% 2.21/2.50  479 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_sup__absorb1_0) # label(axiom).  [assumption].
% 2.21/2.50  480 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom).  [assumption].
% 2.21/2.50  481 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom).  [assumption].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(C,A)),tc_fun(C,A)),D)).  [resolve(460,a,461,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(C,A)),tc_fun(C,A)),D)).  [resolve(460,a,462,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)).  [resolve(460,a,463,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),E)).  [resolve(460,a,464,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),D)).  [resolve(460,a,467,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),E)).  [resolve(460,a,468,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),E)).  [resolve(460,a,469,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,A)))).  [resolve(460,a,470,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,A)))).  [resolve(460,a,471,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B.  [resolve(460,a,474,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)).  [resolve(460,a,475,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)).  [resolve(460,a,476,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)).  [resolve(460,a,477,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)).  [resolve(460,a,478,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),B)).  [resolve(460,a,479,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)).  [resolve(460,a,480,a)].
% 2.21/2.50  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)).  [resolve(460,a,481,a)].
% 2.21/2.50  482 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat),B)).  [resolve(482,a,461,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),tc_nat),B)).  [resolve(482,a,462,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(482,a,463,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(482,a,464,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)).  [resolve(482,a,467,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(482,a,468,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(482,a,469,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))).  [resolve(482,a,470,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))).  [resolve(482,a,471,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A.  [resolve(482,a,474,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat).  [resolve(482,a,475,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat).  [resolve(482,a,476,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(482,a,477,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(c_lessequals(A,tc_nat),B)).  [resolve(482,a,478,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)).  [resolve(482,a,479,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat).  [resolve(482,a,480,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat).  [resolve(482,a,481,a)].
% 2.21/2.50  483 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool),B)).  [resolve(483,a,461,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),tc_bool),B)).  [resolve(483,a,462,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(483,a,463,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)).  [resolve(483,a,464,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),B)).  [resolve(483,a,467,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),C)).  [resolve(483,a,468,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(B,tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)).  [resolve(483,a,469,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))).  [resolve(483,a,470,a)].
% 2.21/2.50  Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))).  [resolve(483,a,471,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A.  [resolve(483,a,474,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool).  [resolve(483,a,475,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool).  [resolve(483,a,476,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(483,a,477,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(c_lessequals(A,tc_bool),B)).  [resolve(483,a,478,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)).  [resolve(483,a,479,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool).  [resolve(483,a,480,a)].
% 2.21/2.50  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool).  [resolve(483,a,481,a)].
% 2.21/2.50  484 class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(484,a,461,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(484,a,462,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(484,a,463,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(484,a,464,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)).  [resolve(484,a,467,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(484,a,468,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(484,a,469,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal))).  [resolve(484,a,470,a)].
% 2.21/2.53  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal))).  [resolve(484,a,471,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_RealDef_Oreal) = A.  [resolve(484,a,474,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(484,a,475,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(484,a,476,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = B | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(484,a,477,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) != B | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)).  [resolve(484,a,478,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = A | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),A)).  [resolve(484,a,479,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal).  [resolve(484,a,480,a)].
% 2.21/2.53  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal).  [resolve(484,a,481,a)].
% 2.21/2.53  485 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom).  [assumption].
% 2.21/2.53  486 -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].
% 2.21/2.53  487 -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].
% 2.21/2.53  488 -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].
% 2.21/2.53  489 -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].
% 2.21/2.53  490 -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].
% 2.21/2.53  491 -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].
% 2.21/2.53  492 -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].
% 2.21/2.53  493 -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].
% 2.21/2.53  494 -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].
% 2.21/2.53  495 -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].
% 2.21/2.53  496 -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].
% 2.21/2.53  497 -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].
% 2.21/2.53  498 -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].
% 2.21/2.53  499 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom).  [assumption].
% 2.21/2.53  500 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom).  [assumption].
% 2.21/2.53  501 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom).  [assumption].
% 2.21/2.53  502 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom).  [assumption].
% 2.21/2.53  503 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom).  [assumption].
% 2.21/2.53  504 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom).  [assumption].
% 2.21/2.53  505 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom).  [assumption].
% 2.21/2.53  506 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom).  [assumption].
% 2.21/2.53  507 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom).  [assumption].
% 2.21/2.53  508 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom).  [assumption].
% 2.21/2.53  509 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom).  [assumption].
% 2.21/2.53  510 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom).  [assumption].
% 2.21/2.53  511 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom).  [assumption].
% 2.21/2.53  512 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom).  [assumption].
% 2.21/2.53  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(C,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),D)).  [resolve(485,a,486,a)].
% 2.21/2.53  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(485,a,488,a)].
% 2.21/2.53  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(485,a,489,a)].
% 2.21/2.53  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(485,a,491,a)].
% 2.21/2.53  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(485,a,492,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A).  [resolve(485,a,494,a)].
% 2.21/2.53  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(485,a,496,a)].
% 2.21/2.53  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(485,a,497,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),B).  [resolve(485,a,499,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B)),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)).  [resolve(485,a,500,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)).  [resolve(485,a,501,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A.  [resolve(485,a,502,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A.  [resolve(485,a,503,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).  [resolve(485,a,505,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)).  [resolve(485,a,507,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C).  [resolve(485,a,508,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B).  [resolve(485,a,510,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).  [resolve(485,a,511,a)].
% 2.21/2.53  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).  [resolve(485,a,512,a)].
% 2.21/2.53  513 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom).  [assumption].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),D)).  [resolve(513,a,486,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)).  [resolve(513,a,488,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B).  [resolve(513,a,489,a)].
% 2.21/2.53  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C).  [resolve(513,a,491,a)].
% 2.31/2.56  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)).  [resolve(513,a,492,a)].
% 2.31/2.56  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A).  [resolve(513,a,494,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),B).  [resolve(513,a,499,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A.  [resolve(513,a,502,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A.  [resolve(513,a,503,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),A).  [resolve(513,a,505,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)).  [resolve(513,a,507,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C).  [resolve(513,a,508,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B).  [resolve(513,a,510,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)).  [resolve(513,a,511,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)).  [resolve(513,a,512,a)].
% 2.31/2.56  514 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom).  [assumption].
% 2.31/2.56  515 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),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_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom).  [assumption].
% 2.31/2.56  516 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 2.31/2.56  517 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 2.31/2.56  518 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 2.31/2.56  519 -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))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom).  [assumption].
% 2.31/2.56  520 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -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].
% 2.31/2.56  521 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -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].
% 2.31/2.56  522 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),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_add__nonneg__nonneg_0) # label(axiom).  [assumption].
% 2.31/2.56  523 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),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(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom).  [assumption].
% 2.31/2.56  524 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),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_add__pos__pos_0) # label(axiom).  [assumption].
% 2.31/2.56  525 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(514,a,515,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(514,a,516,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(514,a,517,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(514,a,518,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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)).  [resolve(514,a,520,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -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(514,a,521,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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(514,a,522,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(514,a,523,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),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(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))).  [resolve(514,a,525,a)].
% 2.31/2.56  526 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom).  [assumption].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(526,a,515,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(526,a,516,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(526,a,517,a)].
% 2.31/2.56  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(526,a,518,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(526,a,520,a)].
% 2.31/2.56  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(526,a,521,a)].
% 2.31/2.59  Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)).  [resolve(526,a,522,a)].
% 2.31/2.59  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(526,a,523,a)].
% 2.31/2.59  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).  [resolve(526,a,525,a)].
% 2.31/2.59  527 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).  [assumption].
% 2.31/2.59  528 -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].
% 2.31/2.59  529 -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].
% 2.31/2.59  530 -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].
% 2.31/2.59  531 -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].
% 2.31/2.59  532 -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].
% 2.31/2.59  533 -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].
% 2.31/2.59  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(527,a,528,a)].
% 2.31/2.59  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(527,a,529,a)].
% 2.31/2.59  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(527,a,530,a)].
% 2.41/2.64  534 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom).  [assumption].
% 2.41/2.64  535 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom).  [assumption].
% 2.41/2.64  536 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom).  [assumption].
% 2.41/2.64  537 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) # label(cls_less__eq__neg__nonpos_0) # label(axiom).  [assumption].
% 2.41/2.64  538 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__eq__neg__nonpos_1) # label(axiom).  [assumption].
% 2.41/2.64  539 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) # label(cls_neg__less__eq__nonneg_0) # label(axiom).  [assumption].
% 2.41/2.64  540 -class_OrderedGroup_Oordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_neg__less__eq__nonneg_1) # label(axiom).  [assumption].
% 2.41/2.64  541 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom).  [assumption].
% 2.41/2.64  Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(535,a,536,a)].
% 2.41/2.64  542 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom).  [assumption].
% 2.41/2.64  543 -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].
% 2.41/2.64  544 -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].
% 2.41/2.64  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(542,a,543,a)].
% 2.41/2.64  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(542,a,544,a)].
% 2.41/2.64  545 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom).  [assumption].
% 2.41/2.64  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(545,a,543,a)].
% 2.48/2.72  Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A)) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(545,a,544,a)].
% 2.48/2.72  546 c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal).  [resolve(103,a,105,a)].
% 2.48/2.72  547 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),hAPP(C,D)),hAPP(C,E)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Odiff_0) # label(axiom).  [assumption].
% 2.48/2.72  548 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_Finite__Set_Osetsum(D,E,F,B)) = c_Finite__Set_Osetsum(c_COMBB(C,D,B,A,F),E,F,A) | -c_RealVector_Oadditive(C,B,A) # label(cls_additive_Osetsum_0) # label(axiom).  [assumption].
% 2.48/2.72  549 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),D)) = hAPP(c_HOL_Ouminus__class_Ouminus(B),hAPP(C,D)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Ominus_0) # label(axiom).  [assumption].
% 2.48/2.72  550 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_HOL_Ozero__class_Ozero(B)) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Oadditive(C,B,A) # label(cls_additive_Ozero_0) # label(axiom).  [assumption].
% 2.48/2.72  551 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(B),hAPP(C,D)),hAPP(C,E)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Oadd_0) # label(axiom).  [assumption].
% 2.48/2.72  Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)).  [resolve(546,a,547,d)].
% 2.48/2.72  Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal).  [resolve(546,a,548,d)].
% 2.48/2.72  Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)).  [resolve(546,a,549,d)].
% 2.48/2.72  Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(546,a,550,d)].
% 2.48/2.72  Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)).  [resolve(546,a,551,d)].
% 2.53/2.79  552 c_RealVector_Oadditive(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal).  [resolve(317,a,318,a)].
% 2.53/2.79  553 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom).  [assumption].
% 2.53/2.79  554 -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].
% 2.53/2.79  555 -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].
% 2.53/2.79  556 -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].
% 2.53/2.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).  [resolve(553,a,554,a)].
% 2.53/2.79  557 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom).  [assumption].
% 2.53/2.79  558 -class_Ring__and__Field_Ono__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_no__zero__divisors_0) # label(axiom).  [assumption].
% 2.53/2.79  559 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom).  [assumption].
% 2.53/2.79  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(557,a,558,a)].
% 2.53/2.79  560 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom).  [assumption].
% 2.53/2.79  561 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom).  [assumption].
% 2.53/2.79  562 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Odiff_0) # label(axiom).  [assumption].
% 2.53/2.79  563 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),D,A) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_OscaleR_0) # label(axiom).  [assumption].
% 2.53/2.79  564 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oinverse__class_Odivide(B,C,A)) # label(cls_divide_Ominus_0) # label(axiom).  [assumption].
% 2.53/2.79  565 -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].
% 2.53/2.79  566 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Oadd_0) # label(axiom).  [assumption].
% 2.53/2.79  Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),C,tc_RealDef_Oreal) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)).  [resolve(561,a,563,a)].
% 2.53/2.83  Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)).  [resolve(561,a,564,a)].
% 2.53/2.83  567 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom).  [assumption].
% 2.53/2.83  568 -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].
% 2.53/2.83  569 -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].
% 2.53/2.83  570 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom).  [assumption].
% 2.53/2.83  571 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 2.53/2.83  572 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -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].
% 2.53/2.83  573 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -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].
% 2.53/2.83  574 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -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].
% 2.53/2.83  575 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -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].
% 2.53/2.83  576 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__cancel__right_1) # label(axiom).  [assumption].
% 2.53/2.83  577 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom).  [assumption].
% 2.53/2.83  578 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__less__cancel__left_1) # label(axiom).  [assumption].
% 2.53/2.84  579 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom).  [assumption].
% 2.53/2.84  580 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__cancel__right_1) # label(axiom).  [assumption].
% 2.53/2.84  581 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom).  [assumption].
% 2.53/2.84  582 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__le__cancel__left_1) # label(axiom).  [assumption].
% 2.53/2.84  583 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom).  [assumption].
% 2.53/2.84  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)).  [resolve(571,a,572,a)].
% 2.53/2.84  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)).  [resolve(571,a,573,a)].
% 2.53/2.84  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -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(571,a,574,a)].
% 2.53/2.84  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -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(571,a,575,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(571,a,576,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))).  [resolve(571,a,577,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)).  [resolve(571,a,578,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))).  [resolve(571,a,579,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(571,a,580,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))).  [resolve(571,a,581,a)].
% 2.53/2.84  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)).  [resolve(571,a,582,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))).  [resolve(571,a,583,a)].
% 2.53/2.86  584 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom).  [assumption].
% 2.53/2.86  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),C)).  [resolve(584,a,572,a)].
% 2.53/2.86  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(584,a,573,a)].
% 2.53/2.86  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(584,a,574,a)].
% 2.53/2.86  Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B)).  [resolve(584,a,575,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(584,a,576,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))).  [resolve(584,a,577,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),C)).  [resolve(584,a,578,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))).  [resolve(584,a,579,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(584,a,580,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C))).  [resolve(584,a,581,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),C)).  [resolve(584,a,582,a)].
% 2.53/2.86  Derived: hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))).  [resolve(584,a,583,a)].
% 2.53/2.86  585 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom).  [assumption].
% 2.53/2.86  586 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),A),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom).  [assumption].
% 2.53/2.86  587 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom).  [assumption].
% 2.53/2.86  588 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom).  [assumption].
% 2.53/2.86  589 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom).  [assumption].
% 2.53/2.86  590 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom).  [assumption].
% 2.53/2.86  591 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  592 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),A),C),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  593 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),A),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  594 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(E,A),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(F,A),D),C,A) # label(cls_mod__mult__cong_0) # label(axiom).  [assumption].
% 2.53/2.86  595 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom).  [assumption].
% 2.53/2.86  596 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom).  [assumption].
% 2.53/2.86  597 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom).  [assumption].
% 2.53/2.86  598 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom).  [assumption].
% 2.53/2.86  599 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom).  [assumption].
% 2.53/2.86  600 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Divides_Odiv__class_Omod(C,D,A)) # label(cls_mod__mult__mult1_0) # label(axiom).  [assumption].
% 2.53/2.86  601 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(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_Divides_Odiv__class_Omod(B,D,A),A),C) # label(cls_mod__mult__mult2_0) # label(axiom).  [assumption].
% 2.53/2.86  602 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom).  [assumption].
% 2.53/2.86  603 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom).  [assumption].
% 2.53/2.86  604 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom).  [assumption].
% 2.53/2.86  605 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom).  [assumption].
% 2.53/2.86  606 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  607 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  608 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom).  [assumption].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),B,tc_nat).  [resolve(585,a,586,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(585,a,587,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat).  [resolve(585,a,588,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A.  [resolve(585,a,589,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(585,a,590,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat).  [resolve(585,a,591,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),B),C,tc_nat).  [resolve(585,a,592,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat).  [resolve(585,a,593,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(D,tc_nat),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(E,tc_nat),C),B,tc_nat).  [resolve(585,a,594,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat).  [resolve(585,a,595,a)].
% 2.53/2.86  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat).  [resolve(585,a,596,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat).  [resolve(585,a,597,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(585,a,598,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat).  [resolve(585,a,599,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat)).  [resolve(585,a,600,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(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_Divides_Odiv__class_Omod(A,C,tc_nat),tc_nat),B).  [resolve(585,a,601,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).  [resolve(585,a,602,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat).  [resolve(585,a,603,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat).  [resolve(585,a,604,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat).  [resolve(585,a,605,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat).  [resolve(585,a,606,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat).  [resolve(585,a,607,a)].
% 2.66/2.91  Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat).  [resolve(585,a,608,a)].
% 2.66/2.91  609 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom).  [assumption].
% 2.66/2.91  610 -class_Ring__and__Field_Osemiring__0(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom).  [assumption].
% 2.66/2.91  Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_nat),B,tc_nat,tc_nat,D),C,D,tc_nat).  [resolve(609,a,610,a)].
% 2.66/2.91  611 class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) # label(axiom).  [assumption].
% 2.66/2.91  612 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom).  [assumption].
% 2.66/2.91  613 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__scaleR__left_0) # label(axiom).  [assumption].
% 2.66/2.91  614 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__scaleR__right_0) # label(axiom).  [assumption].
% 2.76/3.02  615 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom).  [assumption].
% 2.76/3.02  616 -class_RealVector_Oreal__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)),F,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E),F,A))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),F,A),A),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom).  [assumption].
% 2.76/3.02  Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)),E,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),B),D),E,tc_RealDef_Oreal))),hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_RealDef_Oreal),A),C),E,tc_RealDef_Oreal),tc_RealDef_Oreal),D)).  [resolve(615,a,616,a)].
% 2.76/3.02  617 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom).  [assumption].
% 2.76/3.02  618 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom).  [assumption].
% 2.76/3.02  619 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom).  [assumption].
% 2.76/3.02  620 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom).  [assumption].
% 2.76/3.02  621 -class_OrderedGroup_Osemigroup__add(A) | c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A) # label(cls_semigroup__add__class_Oaxioms_0) # label(axiom).  [assumption].
% 2.76/3.02  622 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_OrderedGroup_Osemigroup__add(A,E) # label(cls_semigroup__add_Oadd__assoc_0) # label(axiom).  [assumption].
% 2.76/3.02  Derived: -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).  [resolve(621,b,622,b)].
% 2.76/3.02  623 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom).  [assumption].
% 2.76/3.02  624 -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].
% 2.76/3.02  625 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom).  [assumption].
% 2.76/3.02  626 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 2.76/3.02  627 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -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].
% 2.76/3.04  628 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -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].
% 2.76/3.04  629 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom).  [assumption].
% 2.76/3.04  630 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom).  [assumption].
% 2.76/3.04  631 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -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].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(626,a,627,a)].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(626,a,628,a)].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)).  [resolve(626,a,631,a)].
% 2.76/3.04  632 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom).  [assumption].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(632,a,627,a)].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(632,a,628,a)].
% 2.76/3.04  Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_RealDef_Oreal),C)).  [resolve(632,a,631,a)].
% 2.76/3.04  633 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 2.76/3.04  634 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I39_J_0) # label(axiom).  [assumption].
% 2.76/3.04  635 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I38_J_0) # label(axiom).  [assumption].
% 2.83/3.09  636 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom).  [assumption].
% 2.83/3.09  Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11).  [resolve(633,b,634,a)].
% 2.83/3.09  Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12).  [resolve(633,b,635,a)].
% 2.83/3.09  Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).  [resolve(633,b,636,a)].
% 2.83/3.09  637 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 2.83/3.09  638 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom).  [assumption].
% 2.83/3.09  639 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom).  [assumption].
% 2.83/3.09  640 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom).  [assumption].
% 2.83/3.09  641 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom).  [assumption].
% 2.83/3.09  642 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom).  [assumption].
% 2.83/3.09  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)).  [resolve(639,a,640,a)].
% 2.83/3.09  643 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom).  [assumption].
% 2.83/3.09  Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_RealDef_Oreal),D)) | -hBOOL(hAPP(c_lessequals(A,tc_RealDef_Oreal),C)).  [resolve(643,a,640,a)].
% 2.83/3.09  644 class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom).  [assumption].
% 2.83/3.09  645 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__inf__distrib__right_0) # label(axiom).  [assumption].
% 2.83/3.09  646 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__inf__distrib__left_0) # label(axiom).  [assumption].
% 2.93/3.17  647 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom).  [assumption].
% 2.93/3.17  648 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom).  [assumption].
% 2.93/3.17  649 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom).  [assumption].
% 2.93/3.17  650 class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) # label(axiom).  [assumption].
% 2.93/3.17  651 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__sup__distrib__right_0) # label(axiom).  [assumption].
% 2.93/3.17  652 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__sup__distrib__left_0) # label(axiom).  [assumption].
% 2.93/3.17  653 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Osemigroup__add) # label(axiom).  [assumption].
% 2.93/3.17  654 -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I40_J_0) # label(axiom).  [assumption].
% 2.93/3.17  655 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom).  [assumption].
% 2.93/3.17  656 class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) # label(axiom).  [assumption].
% 2.93/3.17  657 -class_OrderedGroup_Osemigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).  [resolve(621,b,622,b)].
% 2.93/3.17  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).  [resolve(657,a,655,a)].
% 2.93/3.17  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)).  [resolve(657,a,656,a)].
% 2.93/3.17  658 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 2.93/3.17  659 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(A),A) # label(cls_cancel__ab__semigroup__add__class_Oaxioms_0) # label(axiom).  [assumption].
% 2.93/3.17  660 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom).  [assumption].
% 2.93/3.17  Derived: c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat).  [resolve(658,a,659,a)].
% 2.93/3.17  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C.  [resolve(658,a,660,a)].
% 2.93/3.17  661 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom).  [assumption].
% 3.09/3.34  Derived: c_OrderedGroup_Ocancel__ab__semigroup__add__axioms(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),tc_RealDef_Oreal).  [resolve(661,a,659,a)].
% 3.09/3.34  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C.  [resolve(661,a,660,a)].
% 3.09/3.34  662 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Omonoid__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 3.09/3.34  663 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom).  [assumption].
% 3.09/3.34  664 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom).  [assumption].
% 3.09/3.34  Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B.  [resolve(662,b,663,a)].
% 3.09/3.34  Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B.  [resolve(662,b,664,a)].
% 3.09/3.34  665 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 3.09/3.34  666 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom).  [assumption].
% 3.09/3.34  667 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.09/3.34  668 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom).  [assumption].
% 3.09/3.34  669 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom).  [assumption].
% 3.09/3.34  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C.  [resolve(667,a,668,a)].
% 3.09/3.34  670 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom).  [assumption].
% 3.09/3.34  Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C.  [resolve(670,a,668,a)].
% 3.09/3.34  671 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom).  [assumption].
% 3.09/3.34  672 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom).  [assumption].
% 3.09/3.34  Derived: A = A.  [resolve(671,b,672,a)].
% 3.09/3.34  
% 3.09/3.34  ============================== end predicate elimination =============
% 3.09/3.34  
% 3.09/3.34  Auto_denials:  (non-Horn, no changes).
% 3.09/3.34  
% 3.09/3.34  Term ordering decisions:
% 3.09/3.34  Function symbol KB weights:  tc_RealDef_Oreal=1. tc_nat=1. tc_bool=1. c_Suc=1. v_x=1. t_a=1. v_f=1. v_g=1. v_n=1. t_b=1. v_m=1. t_c=1. hAPP=1. c_lessequals=1. c_HOL_Oord__class_Oless=1. c_HOL_Otimes__class_Otimes=1. tc_fun=1. c_RealVector_OscaleR__class_OscaleR=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OlessThan=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Ominus__class_Ominus=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_HOL_Oinverse__class_Odivide=1. c_Divides_Odiv__class_Omod=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanLessThan=1. c_Finite__Set_Osetsum=1. c_Fun_Ocomp=1. c_COMBB=1. c_Fun_Ofcomp=1. c_COMBS=1. c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1=1. c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1=1.
% 3.09/3.34  
% 3.09/3.34  ============================== end of process initial clauses ========
% 3.09/3.34  
% 3.09/3.34  ============================== CLAUSES FOR SECputime limit exceeded (core dumped)
%------------------------------------------------------------------------------