TSTP Solution File: ANA041-1 by Prover9---1109a

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Thu Jul 14 19:21:58 EDT 2022

% Result   : Unsatisfiable 22.83s 22.90s
% Output   : Refutation 22.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 05:58:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.47/1.74  ============================== Prover9 ===============================
% 1.47/1.74  Prover9 (32) version 2009-11A, November 2009.
% 1.47/1.74  Process 5016 was started by sandbox2 on n028.cluster.edu,
% 1.47/1.74  Fri Jul  8 05:58:25 2022
% 1.47/1.74  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4670_n028.cluster.edu".
% 1.47/1.74  ============================== end of head ===========================
% 1.47/1.74  
% 1.47/1.74  ============================== INPUT =================================
% 1.47/1.74  
% 1.47/1.74  % Reading from file /tmp/Prover9_4670_n028.cluster.edu
% 1.47/1.74  
% 1.47/1.74  set(prolog_style_variables).
% 1.47/1.74  set(auto2).
% 1.47/1.74      % set(auto2) -> set(auto).
% 1.47/1.74      % set(auto) -> set(auto_inference).
% 1.47/1.74      % set(auto) -> set(auto_setup).
% 1.47/1.74      % set(auto_setup) -> set(predicate_elim).
% 1.47/1.74      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.47/1.74      % set(auto) -> set(auto_limits).
% 1.47/1.74      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.47/1.74      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.47/1.74      % set(auto) -> set(auto_denials).
% 1.47/1.74      % set(auto) -> set(auto_process).
% 1.47/1.74      % set(auto2) -> assign(new_constants, 1).
% 1.47/1.74      % set(auto2) -> assign(fold_denial_max, 3).
% 1.47/1.74      % set(auto2) -> assign(max_weight, "200.000").
% 1.47/1.74      % set(auto2) -> assign(max_hours, 1).
% 1.47/1.74      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.47/1.74      % set(auto2) -> assign(max_seconds, 0).
% 1.47/1.74      % set(auto2) -> assign(max_minutes, 5).
% 1.47/1.74      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.47/1.74      % set(auto2) -> set(sort_initial_sos).
% 1.47/1.74      % set(auto2) -> assign(sos_limit, -1).
% 1.47/1.74      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.47/1.74      % set(auto2) -> assign(max_megs, 400).
% 1.47/1.74      % set(auto2) -> assign(stats, some).
% 1.47/1.74      % set(auto2) -> clear(echo_input).
% 1.47/1.74      % set(auto2) -> set(quiet).
% 1.47/1.74      % set(auto2) -> clear(print_initial_clauses).
% 1.47/1.74      % set(auto2) -> clear(print_given).
% 1.47/1.74  assign(lrs_ticks,-1).
% 1.47/1.74  assign(sos_limit,10000).
% 1.47/1.74  assign(order,kbo).
% 1.47/1.74  set(lex_order_vars).
% 1.47/1.74  clear(print_given).
% 1.47/1.74  
% 1.47/1.74  % formulas(sos).  % not echoed (2787 formulas)
% 1.47/1.74  
% 1.47/1.74  ============================== end of input ==========================
% 1.47/1.74  
% 1.47/1.74  % From the command line: assign(max_seconds, 300).
% 1.47/1.74  
% 1.47/1.74  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.47/1.74  
% 1.47/1.74  % Formulas that are not ordinary clauses:
% 1.47/1.74  
% 1.47/1.74  ============================== end of process non-clausal formulas ===
% 1.47/1.74  
% 1.47/1.74  ============================== PROCESS INITIAL CLAUSES ===============
% 1.47/1.74  
% 1.47/1.74  ============================== PREDICATE ELIMINATION =================
% 1.47/1.74  1 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D # label(cls_OrderedGroup_Oadd__left__cancel_0) # label(axiom).  [assumption].
% 1.47/1.74  2 class_OrderedGroup_Ocancel__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_10) # label(axiom).  [assumption].
% 1.47/1.74  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_OrderedGroup_Oab__group__add(D).  [resolve(1,a,2,a)].
% 1.47/1.74  3 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D # label(cls_OrderedGroup_Oadd__right__cancel_0) # label(axiom).  [assumption].
% 1.47/1.74  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_OrderedGroup_Oab__group__add(D).  [resolve(3,a,2,a)].
% 1.47/1.74  4 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom).  [assumption].
% 1.47/1.74  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(4,a,1,a)].
% 1.47/1.74  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(4,a,3,a)].
% 1.47/1.74  5 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom).  [assumption].
% 1.47/1.74  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(5,a,1,a)].
% 1.47/1.74  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(5,a,3,a)].
% 1.47/1.74  6 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom).  [assumption].
% 1.47/1.74  Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(6,b,1,a)].
% 1.47/1.74  Derived: -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(6,b,3,a)].
% 1.47/1.74  7 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(7,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(7,b,3,a)].
% 1.47/1.76  8 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(8,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(8,b,3,a)].
% 1.47/1.76  9 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom).  [assumption].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(9,a,2,a)].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(9,a,4,a)].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(9,a,5,a)].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(9,a,6,b)].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(9,a,7,b)].
% 1.47/1.76  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(9,a,8,b)].
% 1.47/1.76  10 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom).  [assumption].
% 1.47/1.76  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(10,a,2,a)].
% 1.47/1.76  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(10,a,4,a)].
% 1.47/1.76  Derived: class_HOL_Oplus(tc_nat).  [resolve(10,a,5,a)].
% 1.47/1.76  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(10,a,6,b)].
% 1.47/1.76  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(10,a,7,b)].
% 1.47/1.76  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(10,a,8,b)].
% 1.47/1.76  11 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(11,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(11,b,3,a)].
% 1.47/1.76  12 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(12,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(12,b,3,a)].
% 1.47/1.76  13 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(13,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(13,b,3,a)].
% 1.47/1.76  14 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom).  [assumption].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(14,b,1,a)].
% 1.47/1.76  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(14,b,3,a)].
% 1.47/1.76  15 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(15,b,1,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(15,b,3,a)].
% 1.55/1.79  16 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(16,b,1,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(16,b,3,a)].
% 1.55/1.79  17 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(17,b,1,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(17,b,3,a)].
% 1.55/1.79  18 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(18,b,1,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(18,b,3,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(18,b,9,a)].
% 1.55/1.79  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(18,b,10,a)].
% 1.55/1.79  19 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(19,b,1,a)].
% 1.55/1.79  Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(19,b,3,a)].
% 1.55/1.79  20 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(20,b,1,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(20,b,3,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A).  [resolve(20,b,10,a)].
% 1.55/1.79  21 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_17) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(21,b,1,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(21,b,3,a)].
% 1.55/1.79  22 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(22,b,1,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(22,b,3,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(22,b,10,a)].
% 1.55/1.79  23 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) # label(axiom).  [assumption].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(23,b,1,a)].
% 1.55/1.79  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(23,b,3,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(23,b,9,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A).  [resolve(23,b,10,a)].
% 1.60/1.83  24 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(24,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(24,b,3,a)].
% 1.60/1.83  25 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(25,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(25,b,3,a)].
% 1.60/1.83  26 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(26,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(26,b,3,a)].
% 1.60/1.83  27 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(27,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(27,b,3,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(27,b,10,a)].
% 1.60/1.83  28 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(28,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(28,b,3,a)].
% 1.60/1.83  29 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(29,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(29,b,3,a)].
% 1.60/1.83  30 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_5) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(30,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(30,b,3,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(30,b,9,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(30,b,10,a)].
% 1.60/1.83  31 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom).  [assumption].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(31,b,1,a)].
% 1.60/1.83  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(31,b,3,a)].
% 1.60/1.83  32 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_20) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(32,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(32,b,3,a)].
% 1.60/1.87  33 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(33,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(33,b,3,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(33,b,9,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A).  [resolve(33,b,10,a)].
% 1.60/1.87  34 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_14) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(34,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(34,b,3,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A).  [resolve(34,b,10,a)].
% 1.60/1.87  35 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_17) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(35,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(35,b,3,a)].
% 1.60/1.87  36 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(36,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(36,b,3,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(36,b,9,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(36,b,10,a)].
% 1.60/1.87  37 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(37,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(37,b,3,a)].
% 1.60/1.87  38 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(38,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(38,b,3,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(38,b,9,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A).  [resolve(38,b,10,a)].
% 1.60/1.87  39 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_10) # label(axiom).  [assumption].
% 1.60/1.87  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(39,b,1,a)].
% 1.60/1.87  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(39,b,3,a)].
% 1.60/1.87  40 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_14) # label(axiom).  [assumption].
% 1.70/1.99  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(40,b,1,a)].
% 1.70/1.99  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(40,b,3,a)].
% 1.70/1.99  41 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom).  [assumption].
% 1.70/1.99  42 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B) # label(clsarity_fun_11) # label(axiom).  [assumption].
% 1.70/1.99  43 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom).  [assumption].
% 1.70/1.99  44 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom).  [assumption].
% 1.70/1.99  45 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom).  [assumption].
% 1.70/1.99  46 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom).  [assumption].
% 1.70/1.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(41,a,42,a)].
% 1.70/1.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(41,a,43,a)].
% 1.70/1.99  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(41,a,44,a)].
% 1.70/1.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(41,a,45,b)].
% 1.70/1.99  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(41,a,46,b)].
% 1.70/1.99  47 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom).  [assumption].
% 1.70/1.99  48 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom).  [assumption].
% 1.70/1.99  49 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom).  [assumption].
% 1.70/1.99  50 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_9) # label(axiom).  [assumption].
% 1.70/1.99  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(50,b,41,a)].
% 1.70/1.99  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(50,b,47,a)].
% 1.70/1.99  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A).  [resolve(50,b,48,a)].
% 1.70/1.99  51 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_10) # label(axiom).  [assumption].
% 1.70/1.99  52 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_10) # label(axiom).  [assumption].
% 1.70/1.99  53 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) # label(axiom).  [assumption].
% 1.70/1.99  54 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_4) # label(axiom).  [assumption].
% 1.70/1.99  55 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) # label(axiom).  [assumption].
% 1.70/1.99  56 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) # label(axiom).  [assumption].
% 1.77/2.03  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(56,b,41,a)].
% 1.77/2.03  57 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom).  [assumption].
% 1.77/2.03  58 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_14) # label(axiom).  [assumption].
% 1.77/2.03  59 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_15) # label(axiom).  [assumption].
% 1.77/2.03  60 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) # label(axiom).  [assumption].
% 1.77/2.03  61 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) # label(axiom).  [assumption].
% 1.77/2.03  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(61,b,41,a)].
% 1.77/2.03  62 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom).  [assumption].
% 1.77/2.03  63 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom).  [assumption].
% 1.77/2.03  64 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_19) # label(axiom).  [assumption].
% 1.77/2.03  65 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) # label(axiom).  [assumption].
% 1.77/2.03  66 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_26) # label(axiom).  [assumption].
% 1.77/2.03  67 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_25) # label(axiom).  [assumption].
% 1.77/2.03  68 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_4) # label(axiom).  [assumption].
% 1.77/2.03  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(68,b,41,a)].
% 1.77/2.03  69 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_19) # label(axiom).  [assumption].
% 1.77/2.03  70 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_19) # label(axiom).  [assumption].
% 1.77/2.03  71 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) # label(axiom).  [assumption].
% 1.77/2.03  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(71,b,41,a)].
% 1.77/2.03  72 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_13) # label(axiom).  [assumption].
% 1.77/2.03  73 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_15) # label(axiom).  [assumption].
% 1.77/2.03  74 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_4) # label(axiom).  [assumption].
% 1.77/2.03  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(74,b,41,a)].
% 1.77/2.03  75 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom).  [assumption].
% 1.77/2.04  Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(75,b,41,a)].
% 1.77/2.04  76 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_4) # label(axiom).  [assumption].
% 1.77/2.04  Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(76,b,41,a)].
% 1.77/2.04  77 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_9) # label(axiom).  [assumption].
% 1.77/2.04  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(77,b,41,a)].
% 1.77/2.04  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(77,b,47,a)].
% 1.77/2.04  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(77,b,48,a)].
% 1.77/2.04  78 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_13) # label(axiom).  [assumption].
% 1.77/2.04  79 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(8,b,1,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_OrderedGroup_Oab__group__add(D).  [resolve(79,a,42,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(79,a,43,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(79,a,44,a)].
% 1.77/2.04  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(79,a,45,b)].
% 1.77/2.04  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C).  [resolve(79,a,46,b)].
% 1.77/2.04  80 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(8,b,3,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_OrderedGroup_Oab__group__add(D).  [resolve(80,a,42,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(80,a,43,a)].
% 1.77/2.04  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(80,a,44,a)].
% 1.77/2.04  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(80,a,45,b)].
% 1.77/2.04  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C).  [resolve(80,a,46,b)].
% 1.77/2.04  81 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(9,a,8,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(81,b,42,a)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(81,b,43,a)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(81,b,44,a)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(81,b,45,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(81,b,46,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(81,b,49,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(81,b,51,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(81,b,52,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(81,b,53,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(81,b,54,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(81,b,55,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(81,b,57,b)].
% 1.77/2.04  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(81,b,58,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(81,b,59,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(81,b,60,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(81,b,62,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(81,b,63,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(81,b,64,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(81,b,65,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(81,b,66,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(81,b,67,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(81,b,69,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(81,b,70,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(81,b,72,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(81,b,73,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(81,b,75,b)].
% 1.91/2.16  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(81,b,78,b)].
% 1.91/2.16  82 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A).  [resolve(10,a,8,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(82,b,42,a)].
% 1.91/2.16  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(82,b,43,a)].
% 1.91/2.16  Derived: class_HOL_Oplus(tc_nat).  [resolve(82,b,44,a)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(82,b,45,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(82,b,46,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(82,b,49,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(82,b,51,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(82,b,52,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(82,b,53,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(82,b,54,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(82,b,55,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(82,b,57,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(82,b,59,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(82,b,62,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(82,b,63,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(82,b,64,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(82,b,66,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(82,b,67,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(82,b,69,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(82,b,70,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(82,b,73,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A).  [resolve(82,b,75,b)].
% 1.91/2.16  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(82,b,78,b)].
% 1.91/2.16  83 -class_OrderedGroup_Oab__semigroup__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_0) # label(axiom).  [assumption].
% 1.91/2.19  84 class_OrderedGroup_Oab__semigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_14) # label(axiom).  [assumption].
% 1.91/2.19  85 class_OrderedGroup_Oab__semigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_13) # label(axiom).  [assumption].
% 1.91/2.19  86 class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_9) # label(axiom).  [assumption].
% 1.91/2.19  87 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat_17) # label(axiom).  [assumption].
% 1.91/2.19  88 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom).  [assumption].
% 1.91/2.19  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(83,a,84,a)].
% 1.91/2.19  Derived: class_OrderedGroup_Osemigroup__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(83,a,85,a)].
% 1.91/2.19  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(83,a,86,a)].
% 1.91/2.19  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(83,a,87,a)].
% 1.91/2.19  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(83,a,88,b)].
% 1.91/2.19  89 -class_OrderedGroup_Oab__semigroup__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Oab__semigroup__mult_1) # label(axiom).  [assumption].
% 1.91/2.19  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(89,a,84,a)].
% 1.91/2.19  Derived: class_HOL_Otimes(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(89,a,85,a)].
% 1.91/2.19  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(89,a,86,a)].
% 1.91/2.19  Derived: class_HOL_Otimes(tc_nat).  [resolve(89,a,87,a)].
% 1.91/2.19  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(89,a,88,b)].
% 1.91/2.19  90 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom).  [assumption].
% 1.91/2.19  91 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom).  [assumption].
% 1.91/2.19  Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(91,b,83,a)].
% 1.91/2.19  Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A).  [resolve(91,b,89,a)].
% 1.91/2.19  92 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom).  [assumption].
% 1.91/2.19  93 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_7) # label(axiom).  [assumption].
% 1.91/2.19  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(93,b,83,a)].
% 1.91/2.19  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A).  [resolve(93,b,89,a)].
% 1.91/2.19  94 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom).  [assumption].
% 1.91/2.19  95 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_1) # label(axiom).  [assumption].
% 1.91/2.19  96 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) # label(axiom).  [assumption].
% 1.91/2.19  97 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_5) # label(axiom).  [assumption].
% 1.91/2.19  98 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) # label(axiom).  [assumption].
% 1.91/2.19  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(98,b,83,a)].
% 1.91/2.19  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(98,b,89,a)].
% 1.91/2.19  99 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ofield_17) # label(axiom).  [assumption].
% 2.09/2.35  100 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom).  [assumption].
% 2.09/2.35  101 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) # label(axiom).  [assumption].
% 2.09/2.35  102 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_20) # label(axiom).  [assumption].
% 2.09/2.35  103 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom).  [assumption].
% 2.09/2.35  104 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom).  [assumption].
% 2.09/2.35  105 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) # label(axiom).  [assumption].
% 2.09/2.35  106 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_7) # label(axiom).  [assumption].
% 2.09/2.35  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(106,b,83,a)].
% 2.09/2.35  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | class_HOL_Otimes(A).  [resolve(106,b,89,a)].
% 2.09/2.35  107 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_2) # label(axiom).  [assumption].
% 2.09/2.35  108 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom).  [assumption].
% 2.09/2.35  109 class_OrderedGroup_Omonoid__mult(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B) # label(clsarity_fun_15) # label(axiom).  [assumption].
% 2.09/2.35  110 class_OrderedGroup_Omonoid__mult(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsarity_set_14) # label(axiom).  [assumption].
% 2.09/2.35  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C).  [resolve(108,a,109,a)].
% 2.09/2.35  Derived: c_times(c_1,A,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(108,a,110,a)].
% 2.09/2.35  111 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom).  [assumption].
% 2.09/2.35  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_OrderedGroup_Ocomm__monoid__mult(C).  [resolve(111,a,109,a)].
% 2.09/2.35  Derived: c_times(A,c_1,tc_set(B)) = A | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(111,a,110,a)].
% 2.09/2.35  112 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom).  [assumption].
% 2.09/2.35  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(112,a,108,a)].
% 2.09/2.35  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(112,a,111,a)].
% 2.09/2.35  113 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom).  [assumption].
% 2.09/2.35  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(113,a,108,a)].
% 2.09/2.35  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(113,a,111,a)].
% 2.09/2.35  114 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom).  [assumption].
% 2.09/2.35  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B.  [resolve(114,b,108,a)].
% 2.09/2.35  Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B.  [resolve(114,b,111,a)].
% 2.09/2.35  115 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom).  [assumption].
% 2.09/2.35  Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B.  [resolve(115,b,108,a)].
% 2.09/2.35  Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B.  [resolve(115,b,111,a)].
% 2.09/2.35  116 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom).  [assumption].
% 2.15/2.38  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__mult(B).  [resolve(116,a,109,a)].
% 2.15/2.38  Derived: class_HOL_Oone(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(116,a,110,a)].
% 2.15/2.38  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(116,a,112,a)].
% 2.15/2.38  Derived: class_HOL_Oone(tc_nat).  [resolve(116,a,113,a)].
% 2.15/2.38  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(116,a,114,b)].
% 2.15/2.38  Derived: class_HOL_Oone(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(116,a,115,b)].
% 2.15/2.38  117 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom).  [assumption].
% 2.15/2.38  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(117,a,115,b)].
% 2.15/2.38  118 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom).  [assumption].
% 2.15/2.38  Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(118,a,115,b)].
% 2.15/2.38  119 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B.  [resolve(119,b,108,a)].
% 2.15/2.38  Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B.  [resolve(119,b,111,a)].
% 2.15/2.38  120 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_24) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_1,B,A) = B.  [resolve(120,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_1,A) = B.  [resolve(120,b,111,a)].
% 2.15/2.38  121 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_15) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B.  [resolve(121,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B.  [resolve(121,b,111,a)].
% 2.15/2.38  122 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(122,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(122,b,111,a)].
% 2.15/2.38  123 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B.  [resolve(123,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B.  [resolve(123,b,111,a)].
% 2.15/2.38  124 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B.  [resolve(124,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B.  [resolve(124,b,111,a)].
% 2.15/2.38  125 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B.  [resolve(125,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B.  [resolve(125,b,111,a)].
% 2.15/2.38  126 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom).  [assumption].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B.  [resolve(126,b,108,a)].
% 2.15/2.38  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B.  [resolve(126,b,111,a)].
% 2.15/2.38  127 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B.  [resolve(127,b,108,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B.  [resolve(127,b,111,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(127,b,117,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A).  [resolve(127,b,118,a)].
% 2.26/2.51  128 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B.  [resolve(128,b,108,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B.  [resolve(128,b,111,a)].
% 2.26/2.51  129 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B.  [resolve(129,b,108,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B.  [resolve(129,b,111,a)].
% 2.26/2.51  130 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_9) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(130,b,108,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(130,b,111,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(130,b,116,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(130,b,117,a)].
% 2.26/2.51  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(130,b,118,a)].
% 2.26/2.51  131 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__distrib__number__of_0) # label(axiom).  [assumption].
% 2.26/2.51  132 class_Ring__and__Field_Osemiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_17) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_plus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(131,b,132,a)].
% 2.26/2.51  133 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__distrib__number__of_0) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_plus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(133,b,132,a)].
% 2.26/2.51  134 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom).  [assumption].
% 2.26/2.51  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(134,a,131,b)].
% 2.26/2.51  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(134,a,133,b)].
% 2.31/2.53  135 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(135,a,131,b)].
% 2.31/2.53  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(135,a,133,b)].
% 2.31/2.53  136 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(136,b,131,b)].
% 2.31/2.53  Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(136,b,133,b)].
% 2.31/2.53  137 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Power_Orecpower(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(137,b,131,b)].
% 2.31/2.53  Derived: -class_Power_Orecpower(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(137,b,133,b)].
% 2.31/2.53  138 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(138,b,131,b)].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(138,b,133,b)].
% 2.31/2.53  139 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_10) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(139,b,131,b)].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(139,b,133,b)].
% 2.31/2.53  140 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(140,b,131,b)].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(140,b,133,b)].
% 2.31/2.53  141 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_2) # label(axiom).  [assumption].
% 2.31/2.53  Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(141,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(141,b,133,b)].
% 2.31/2.55  142 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(142,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(142,b,133,b)].
% 2.31/2.55  143 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_7) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(143,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(143,b,133,b)].
% 2.31/2.55  144 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(144,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(144,b,133,b)].
% 2.31/2.55  145 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(145,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(145,b,133,b)].
% 2.31/2.55  146 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(146,b,131,b)].
% 2.31/2.55  Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(146,b,133,b)].
% 2.31/2.55  147 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom).  [assumption].
% 2.31/2.55  Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(147,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(147,b,133,b)].
% 2.31/2.57  148 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(148,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(148,b,133,b)].
% 2.31/2.57  149 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(149,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(149,b,133,b)].
% 2.31/2.57  150 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(150,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(150,b,133,b)].
% 2.31/2.57  151 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_7) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(151,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(151,b,133,b)].
% 2.31/2.57  152 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(152,b,131,b)].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(152,b,133,b)].
% 2.31/2.57  153 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_1) # label(axiom).  [assumption].
% 2.31/2.57  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(153,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(153,b,133,b)].
% 2.31/2.58  154 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(154,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(154,b,133,b)].
% 2.31/2.58  155 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_2) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(155,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(155,b,133,b)].
% 2.31/2.58  156 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_10) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(156,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(156,b,133,b)].
% 2.31/2.58  157 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_4) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(157,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(157,b,133,b)].
% 2.31/2.58  158 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(158,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(158,b,133,b)].
% 2.31/2.58  159 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(159,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(159,b,133,b)].
% 2.31/2.58  160 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(160,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(160,b,133,b)].
% 2.31/2.58  161 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom).  [assumption].
% 2.31/2.58  Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(161,b,131,b)].
% 2.31/2.58  Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(161,b,133,b)].
% 2.31/2.58  162 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom).  [assumption].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(162,a,132,a)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(162,a,137,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(162,a,138,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(162,a,139,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(162,a,140,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(162,a,141,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(162,a,142,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(162,a,143,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(162,a,145,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(162,a,146,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(162,a,147,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(162,a,148,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(162,a,149,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(162,a,150,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(162,a,152,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(162,a,153,b)].
% 2.31/2.58  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(162,a,155,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(162,a,156,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(162,a,157,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(162,a,159,b)].
% 2.31/2.59  163 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom).  [assumption].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(163,a,132,a)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(163,a,140,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(163,a,141,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(163,a,143,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(163,a,157,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(163,a,159,b)].
% 2.31/2.59  164 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom).  [assumption].
% 2.31/2.59  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(164,a,132,a)].
% 2.31/2.59  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(164,a,140,b)].
% 2.31/2.59  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(164,a,141,b)].
% 2.31/2.59  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(164,a,143,b)].
% 2.31/2.59  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(164,a,157,b)].
% 2.31/2.59  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(164,a,159,b)].
% 2.31/2.59  165 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom).  [assumption].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(165,a,132,a)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(165,a,138,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(165,a,140,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(165,a,141,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(165,a,142,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(165,a,143,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(165,a,145,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(165,a,146,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(165,a,147,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(165,a,148,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(165,a,149,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(165,a,150,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(165,a,151,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(165,a,153,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(165,a,154,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(165,a,155,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(165,a,157,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(165,a,158,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(165,a,159,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A).  [resolve(165,a,160,b)].
% 2.31/2.59  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(165,a,161,b)].
% 2.31/2.59  166 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom).  [assumption].
% 2.31/2.59  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(166,a,132,a)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(166,a,138,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(166,a,140,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(166,a,141,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(166,a,142,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(166,a,143,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(166,a,145,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(166,a,146,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(166,a,147,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(166,a,148,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(166,a,149,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(166,a,150,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(166,a,151,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(166,a,153,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(166,a,154,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(166,a,155,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(166,a,157,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(166,a,158,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(166,a,159,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A).  [resolve(166,a,160,b)].
% 2.31/2.59  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(166,a,161,b)].
% 2.31/2.59  167 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom).  [assumption].
% 2.31/2.59  Derived: -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(167,b,131,b)].
% 2.31/2.59  Derived: -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(167,b,133,b)].
% 2.31/2.59  168 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_1) # label(axiom).  [assumption].
% 2.31/2.59  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(168,b,131,b)].
% 2.31/2.59  Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(168,b,133,b)].
% 2.45/2.74  169 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom).  [assumption].
% 2.45/2.74  Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(169,b,131,b)].
% 2.45/2.74  Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(169,b,133,b)].
% 2.45/2.74  Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A).  [resolve(169,b,164,a)].
% 2.45/2.74  170 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_3) # label(axiom).  [assumption].
% 2.45/2.74  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(170,b,131,b)].
% 2.45/2.74  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(170,b,133,b)].
% 2.45/2.74  171 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom).  [assumption].
% 2.45/2.74  172 class_Ring__and__Field_Ocomm__semiring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_18) # label(axiom).  [assumption].
% 2.45/2.74  173 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom).  [assumption].
% 2.45/2.74  174 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom).  [assumption].
% 2.45/2.74  175 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom).  [assumption].
% 2.45/2.74  176 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom).  [assumption].
% 2.45/2.74  177 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_1) # label(axiom).  [assumption].
% 2.45/2.74  178 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_6) # label(axiom).  [assumption].
% 2.45/2.74  179 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom).  [assumption].
% 2.45/2.74  180 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom).  [assumption].
% 2.45/2.74  181 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom).  [assumption].
% 2.45/2.74  182 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom).  [assumption].
% 2.45/2.74  183 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_0) # label(axiom).  [assumption].
% 2.45/2.74  184 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) # label(axiom).  [assumption].
% 2.45/2.74  185 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_4) # label(axiom).  [assumption].
% 2.45/2.74  186 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) # label(axiom).  [assumption].
% 2.54/2.79  187 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom).  [assumption].
% 2.54/2.79  188 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom).  [assumption].
% 2.54/2.79  189 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) # label(axiom).  [assumption].
% 2.54/2.79  190 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_19) # label(axiom).  [assumption].
% 2.54/2.79  191 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_16) # label(axiom).  [assumption].
% 2.54/2.79  192 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_10) # label(axiom).  [assumption].
% 2.54/2.79  193 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) # label(axiom).  [assumption].
% 2.54/2.79  194 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_6) # label(axiom).  [assumption].
% 2.54/2.79  195 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_1) # label(axiom).  [assumption].
% 2.54/2.79  196 -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(140,b,131,b)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_plus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(196,a,172,a)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(196,a,173,a)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(196,a,174,a)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(196,a,175,b)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A).  [resolve(196,a,176,b)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(196,a,177,b)].
% 2.54/2.79  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(196,a,178,b)].
% 2.54/2.79  197 -class_Ring__and__Field_Ocomm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(140,b,133,b)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_plus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(197,a,172,a)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(197,a,173,a)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(197,a,174,a)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(197,a,175,b)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A).  [resolve(197,a,176,b)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(197,a,177,b)].
% 2.57/2.80  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(197,a,178,b)].
% 2.57/2.80  198 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(162,a,140,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(198,b,172,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(198,b,173,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(198,b,174,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(198,b,175,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(198,b,176,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(198,b,177,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(198,b,178,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(198,b,186,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(198,b,193,b)].
% 2.57/2.80  199 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(163,a,140,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(199,b,172,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(199,b,173,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(199,b,174,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(199,b,175,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(199,b,176,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(199,b,177,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(199,b,178,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(199,b,184,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(199,b,186,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(199,b,187,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(199,b,188,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(199,b,189,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(199,b,190,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(199,b,191,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(199,b,192,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(199,b,193,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(199,b,194,b)].
% 2.57/2.80  200 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(164,a,140,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(200,b,172,a)].
% 2.57/2.80  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(200,b,173,a)].
% 2.57/2.80  Derived: class_HOL_Oplus(tc_nat).  [resolve(200,b,174,a)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(200,b,175,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(200,b,176,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(200,b,177,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(200,b,178,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(200,b,184,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(200,b,186,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(200,b,187,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(200,b,188,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(200,b,189,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(200,b,190,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(200,b,191,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(200,b,192,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(200,b,193,b)].
% 2.57/2.80  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(200,b,194,b)].
% 2.57/2.80  201 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(165,a,140,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(201,b,172,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(201,b,173,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(201,b,174,a)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(201,b,175,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A).  [resolve(201,b,176,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(201,b,177,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(201,b,178,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(201,b,186,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(201,b,192,b)].
% 2.57/2.80  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(201,b,194,b)].
% 2.57/2.80  202 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A).  [resolve(166,a,140,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(202,b,172,a)].
% 2.73/2.98  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(202,b,173,a)].
% 2.73/2.98  Derived: class_HOL_Otimes(tc_nat).  [resolve(202,b,174,a)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(202,b,175,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A).  [resolve(202,b,176,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(202,b,177,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(202,b,178,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(202,b,186,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(202,b,192,b)].
% 2.73/2.98  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(202,b,194,b)].
% 2.73/2.98  203 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom).  [assumption].
% 2.73/2.98  204 class_Ring__and__Field_Osemiring__0(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_19) # label(axiom).  [assumption].
% 2.73/2.98  205 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom).  [assumption].
% 2.73/2.98  206 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom).  [assumption].
% 2.73/2.98  207 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom).  [assumption].
% 2.73/2.98  208 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom).  [assumption].
% 2.73/2.98  209 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_3) # label(axiom).  [assumption].
% 2.73/2.98  210 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_9) # label(axiom).  [assumption].
% 2.73/2.98  211 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_10) # label(axiom).  [assumption].
% 2.73/2.98  212 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) # label(axiom).  [assumption].
% 2.73/2.98  213 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_6) # label(axiom).  [assumption].
% 2.73/2.98  214 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) # label(axiom).  [assumption].
% 2.73/2.98  215 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom).  [assumption].
% 2.73/2.98  216 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom).  [assumption].
% 2.73/2.98  217 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Olordered__ring_13) # label(axiom).  [assumption].
% 2.73/2.98  218 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) # label(axiom).  [assumption].
% 2.73/2.98  219 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_22) # label(axiom).  [assumption].
% 2.73/2.98  220 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_19) # label(axiom).  [assumption].
% 2.73/2.98  221 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_6) # label(axiom).  [assumption].
% 2.73/2.98  222 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_13) # label(axiom).  [assumption].
% 2.73/2.99  223 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_0) # label(axiom).  [assumption].
% 2.73/2.99  224 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) # label(axiom).  [assumption].
% 2.73/2.99  225 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_1) # label(axiom).  [assumption].
% 2.73/2.99  226 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_9) # label(axiom).  [assumption].
% 2.73/2.99  227 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_3) # label(axiom).  [assumption].
% 2.73/2.99  228 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__ring_6) # label(axiom).  [assumption].
% 2.73/2.99  229 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Opordered__semiring_0) # label(axiom).  [assumption].
% 2.73/2.99  230 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom).  [assumption].
% 2.73/2.99  231 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring__1_6) # label(axiom).  [assumption].
% 2.73/2.99  232 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom).  [assumption].
% 2.73/2.99  233 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom).  [assumption].
% 2.73/2.99  234 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom).  [assumption].
% 2.73/2.99  235 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom).  [assumption].
% 2.73/2.99  236 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom).  [assumption].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(236,a,204,a)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(236,a,205,a)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(236,a,206,a)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(236,a,207,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A).  [resolve(236,a,208,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(236,a,209,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(236,a,210,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(236,a,211,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(236,a,212,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(236,a,213,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(236,a,214,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(236,a,215,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(236,a,216,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(236,a,217,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(236,a,218,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(236,a,219,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(236,a,220,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(236,a,221,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(236,a,222,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(236,a,223,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(236,a,224,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(236,a,225,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(236,a,226,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(236,a,227,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(236,a,228,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(236,a,229,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(236,a,230,b)].
% 2.73/2.99  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(236,a,231,b)].
% 2.73/2.99  237 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom).  [assumption].
% 2.73/2.99  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(237,a,204,a)].
% 2.73/2.99  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(237,a,205,a)].
% 2.73/2.99  Derived: class_HOL_Ozero(tc_nat).  [resolve(237,a,206,a)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(237,a,207,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(237,a,208,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(237,a,209,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(237,a,210,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(237,a,211,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(237,a,212,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(237,a,213,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(237,a,214,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(237,a,215,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(237,a,216,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(237,a,217,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(237,a,218,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(237,a,219,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(237,a,220,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(237,a,221,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(237,a,222,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(237,a,223,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(237,a,224,b)].
% 2.73/2.99  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(237,a,225,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(237,a,226,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(237,a,227,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(237,a,228,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(237,a,229,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A).  [resolve(237,a,230,b)].
% 2.73/3.03  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(237,a,231,b)].
% 2.73/3.03  238 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_0) # label(axiom).  [assumption].
% 2.73/3.03  239 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1_3) # label(axiom).  [assumption].
% 2.73/3.03  Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A).  [resolve(239,b,237,a)].
% 2.73/3.03  240 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_2) # label(axiom).  [assumption].
% 2.73/3.03  241 -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(167,b,131,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(241,a,211,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(241,a,212,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(241,a,213,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(241,a,214,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(241,a,215,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(241,a,216,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(241,a,217,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(241,a,218,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(241,a,219,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(241,a,220,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(241,a,221,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(241,a,222,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(241,a,223,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(241,a,224,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(241,a,225,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(241,a,226,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(241,a,227,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(241,a,228,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(241,a,229,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A).  [resolve(241,a,230,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A).  [resolve(241,a,231,b)].
% 2.73/3.03  242 -class_Ring__and__Field_Osemiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(167,b,133,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(242,a,211,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(242,a,212,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(242,a,213,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(242,a,214,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(242,a,215,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(242,a,216,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(242,a,217,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(242,a,218,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(242,a,219,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(242,a,220,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(242,a,221,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(242,a,222,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(242,a,223,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(242,a,224,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(242,a,225,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(242,a,226,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(242,a,227,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(242,a,228,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(242,a,229,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A).  [resolve(242,a,230,b)].
% 2.73/3.03  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A).  [resolve(242,a,231,b)].
% 2.92/3.17  243 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_3) # label(axiom).  [assumption].
% 2.92/3.17  244 class_Ring__and__Field_Ocomm__semiring__0(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_20) # label(axiom).  [assumption].
% 2.92/3.17  245 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom).  [assumption].
% 2.92/3.17  246 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom).  [assumption].
% 2.92/3.17  247 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom).  [assumption].
% 2.92/3.17  248 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom).  [assumption].
% 2.92/3.17  249 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring_0) # label(axiom).  [assumption].
% 2.92/3.17  250 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_5) # label(axiom).  [assumption].
% 2.92/3.17  251 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_4) # label(axiom).  [assumption].
% 2.92/3.17  252 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom).  [assumption].
% 2.92/3.17  253 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_6) # label(axiom).  [assumption].
% 2.92/3.17  254 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom).  [assumption].
% 2.92/3.17  255 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_8) # label(axiom).  [assumption].
% 2.92/3.17  256 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom).  [assumption].
% 2.92/3.17  257 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) # label(axiom).  [assumption].
% 2.92/3.17  258 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_3) # label(axiom).  [assumption].
% 2.92/3.17  259 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) # label(axiom).  [assumption].
% 2.92/3.17  260 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom).  [assumption].
% 2.92/3.17  261 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom).  [assumption].
% 2.92/3.17  262 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) # label(axiom).  [assumption].
% 2.92/3.17  263 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__field_18) # label(axiom).  [assumption].
% 2.92/3.17  264 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__idom_15) # label(axiom).  [assumption].
% 2.92/3.17  265 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_9) # label(axiom).  [assumption].
% 2.92/3.17  266 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) # label(axiom).  [assumption].
% 2.99/3.22  267 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_5) # label(axiom).  [assumption].
% 2.99/3.22  268 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_0) # label(axiom).  [assumption].
% 2.99/3.22  269 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(141,b,131,b)].
% 2.99/3.22  270 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(141,b,133,b)].
% 2.99/3.22  271 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(162,a,141,b)].
% 2.99/3.22  272 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(163,a,141,b)].
% 2.99/3.22  273 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(164,a,141,b)].
% 2.99/3.22  274 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(165,a,141,b)].
% 2.99/3.22  275 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(166,a,141,b)].
% 2.99/3.22  276 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(236,a,211,b)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(276,b,244,a)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(276,b,245,a)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(276,b,246,a)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(276,b,247,b)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A).  [resolve(276,b,248,b)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(276,b,249,b)].
% 2.99/3.22  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(276,b,250,b)].
% 2.99/3.22  277 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(237,a,211,b)].
% 2.99/3.22  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(277,b,244,a)].
% 2.99/3.22  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(277,b,245,a)].
% 2.99/3.22  Derived: class_HOL_Ozero(tc_nat).  [resolve(277,b,246,a)].
% 2.99/3.22  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(277,b,247,b)].
% 2.99/3.22  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(277,b,248,b)].
% 2.99/3.22  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(277,b,249,b)].
% 2.99/3.22  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(277,b,250,b)].
% 2.99/3.22  278 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(241,a,211,b)].
% 2.99/3.22  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_plus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(278,c,244,a)].
% 2.99/3.22  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(278,c,245,a)].
% 2.99/3.22  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(278,c,246,a)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(278,c,247,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Power_Orecpower(A).  [resolve(278,c,248,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(278,c,249,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(278,c,250,b)].
% 3.03/3.33  279 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A).  [resolve(242,a,211,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_plus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(279,c,244,a)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(279,c,245,a)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(279,c,246,a)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(279,c,247,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Power_Orecpower(A).  [resolve(279,c,248,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(279,c,249,b)].
% 3.03/3.33  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(279,c,250,b)].
% 3.03/3.33  280 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(c_0,B,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__left_0) # label(axiom).  [assumption].
% 3.03/3.33  281 class_Ring__and__Field_Osemiring__0__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_21) # label(axiom).  [assumption].
% 3.03/3.33  Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(280,a,281,a)].
% 3.03/3.33  282 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(B,c_0,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__right_0) # label(axiom).  [assumption].
% 3.03/3.33  Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(282,a,281,a)].
% 3.03/3.33  283 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom).  [assumption].
% 3.13/3.37  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(283,a,280,a)].
% 3.13/3.37  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(283,a,282,a)].
% 3.13/3.37  284 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom).  [assumption].
% 3.13/3.37  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(284,a,280,a)].
% 3.13/3.37  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(284,a,282,a)].
% 3.13/3.37  285 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(285,b,280,a)].
% 3.13/3.37  Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(285,b,282,a)].
% 3.13/3.37  286 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0.  [resolve(286,b,280,a)].
% 3.13/3.37  Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0.  [resolve(286,b,282,a)].
% 3.13/3.37  287 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring_17) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(287,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(287,b,282,a)].
% 3.13/3.37  288 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_8) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(288,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(288,b,282,a)].
% 3.13/3.37  289 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(289,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(289,b,282,a)].
% 3.13/3.37  290 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(290,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(290,b,282,a)].
% 3.13/3.37  291 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0.  [resolve(291,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0.  [resolve(291,b,282,a)].
% 3.13/3.37  292 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0.  [resolve(292,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0.  [resolve(292,b,282,a)].
% 3.13/3.37  293 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Olordered__ring_12) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(293,b,280,a)].
% 3.13/3.37  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(293,b,282,a)].
% 3.13/3.37  294 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) # label(axiom).  [assumption].
% 3.13/3.37  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(294,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(294,b,282,a)].
% 3.13/3.39  295 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_21) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0.  [resolve(295,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0.  [resolve(295,b,282,a)].
% 3.13/3.39  296 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_18) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0.  [resolve(296,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0.  [resolve(296,b,282,a)].
% 3.13/3.39  297 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_3) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(297,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(297,b,282,a)].
% 3.13/3.39  298 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_12) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0.  [resolve(298,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0.  [resolve(298,b,282,a)].
% 3.13/3.39  299 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_21) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(299,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(299,b,282,a)].
% 3.13/3.39  300 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(300,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(300,b,282,a)].
% 3.13/3.39  301 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_15) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(301,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(301,b,282,a)].
% 3.13/3.39  302 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_8) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(302,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(302,b,282,a)].
% 3.13/3.39  303 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__ring_3) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(303,b,280,a)].
% 3.13/3.39  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(303,b,282,a)].
% 3.13/3.39  304 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom).  [assumption].
% 3.13/3.39  Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0.  [resolve(304,b,280,a)].
% 3.17/3.42  Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0.  [resolve(304,b,282,a)].
% 3.17/3.42  305 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring__1_3) # label(axiom).  [assumption].
% 3.17/3.42  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(305,b,280,a)].
% 3.17/3.42  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(305,b,282,a)].
% 3.17/3.42  306 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_2) # label(axiom).  [assumption].
% 3.17/3.42  307 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom).  [assumption].
% 3.17/3.42  308 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_4) # label(axiom).  [assumption].
% 3.17/3.42  309 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_5) # label(axiom).  [assumption].
% 3.17/3.42  310 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_6) # label(axiom).  [assumption].
% 3.17/3.42  311 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom).  [assumption].
% 3.17/3.42  312 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom).  [assumption].
% 3.17/3.42  313 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_15) # label(axiom).  [assumption].
% 3.17/3.42  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(313,b,280,a)].
% 3.17/3.42  Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(313,b,282,a)].
% 3.17/3.42  314 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(39,b,1,a)].
% 3.17/3.42  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(314,a,281,a)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C).  [resolve(314,a,286,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(314,a,287,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(314,a,288,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C).  [resolve(314,a,289,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C).  [resolve(314,a,290,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(314,a,291,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(314,a,292,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(314,a,293,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(314,a,294,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(314,a,295,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(314,a,296,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(314,a,297,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C).  [resolve(314,a,298,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(314,a,299,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(314,a,300,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(314,a,301,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(314,a,302,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(314,a,303,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C).  [resolve(314,a,304,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C).  [resolve(314,a,305,b)].
% 3.17/3.42  315 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(39,b,3,a)].
% 3.17/3.42  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(315,a,281,a)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C).  [resolve(315,a,286,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(315,a,287,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(315,a,288,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C).  [resolve(315,a,289,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C).  [resolve(315,a,290,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(315,a,291,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(315,a,292,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(315,a,293,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(315,a,294,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(315,a,295,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(315,a,296,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(315,a,297,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C).  [resolve(315,a,298,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(315,a,299,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(315,a,300,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(315,a,301,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(315,a,302,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(315,a,303,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C).  [resolve(315,a,304,b)].
% 3.17/3.42  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C).  [resolve(315,a,305,b)].
% 3.17/3.42  316 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(77,b,41,a)].
% 3.17/3.42  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(316,a,297,b)].
% 3.17/3.42  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(316,a,303,b)].
% 3.17/3.42  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(316,a,304,b)].
% 3.17/3.42  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(316,a,305,b)].
% 3.17/3.42  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(316,a,313,b)].
% 3.17/3.42  317 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(77,b,47,a)].
% 3.32/3.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(317,a,297,b)].
% 3.32/3.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(317,a,303,b)].
% 3.32/3.57  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(317,a,305,b)].
% 3.32/3.57  318 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(77,b,48,a)].
% 3.32/3.57  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(318,a,297,b)].
% 3.32/3.57  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(318,a,301,b)].
% 3.32/3.57  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(318,a,303,b)].
% 3.32/3.57  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(318,a,305,b)].
% 3.32/3.57  319 -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(168,b,131,b)].
% 3.32/3.57  320 -class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(168,b,133,b)].
% 3.32/3.57  321 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__diff__distrib__number__of_0) # label(axiom).  [assumption].
% 3.32/3.57  322 class_Ring__and__Field_Oring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_22) # label(axiom).  [assumption].
% 3.32/3.57  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_minus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(321,b,322,a)].
% 3.32/3.57  323 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__diff__distrib__number__of_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_minus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(323,b,322,a)].
% 3.32/3.57  324 -class_Ring__and__Field_Oring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A) # label(cls_Ring__and__Field_Ominus__mult__minus_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_times(c_uminus(A,tc_fun(B,C)),c_uminus(D,tc_fun(B,C)),tc_fun(B,C)) = c_times(A,D,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(324,a,322,a)].
% 3.32/3.57  325 -class_Ring__and__Field_Oring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A) # label(cls_Ring__and__Field_Omult__minus__left_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_times(c_uminus(A,tc_fun(B,C)),D,tc_fun(B,C)) = c_uminus(c_times(A,D,tc_fun(B,C)),tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(325,a,322,a)].
% 3.32/3.57  326 -class_Ring__and__Field_Oring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A) # label(cls_Ring__and__Field_Omult__minus__right_0) # label(axiom).  [assumption].
% 3.32/3.57  Derived: c_times(A,c_uminus(B,tc_fun(C,D)),tc_fun(C,D)) = c_uminus(c_times(A,B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(326,a,322,a)].
% 3.32/3.57  327 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom).  [assumption].
% 3.32/3.57  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(327,a,321,b)].
% 3.32/3.58  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(327,a,323,b)].
% 3.32/3.58  Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint).  [resolve(327,a,324,a)].
% 3.32/3.58  Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(327,a,325,a)].
% 3.32/3.58  Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(327,a,326,a)].
% 3.32/3.58  328 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom).  [assumption].
% 3.32/3.58  Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(328,b,321,b)].
% 3.32/3.58  Derived: -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(328,b,323,b)].
% 3.32/3.58  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(328,b,324,a)].
% 3.32/3.58  Derived: -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(328,b,325,a)].
% 3.32/3.58  Derived: -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(328,b,326,a)].
% 3.32/3.58  329 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom).  [assumption].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(329,b,321,b)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(329,b,323,b)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(329,b,324,a)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(329,b,325,a)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(329,b,326,a)].
% 3.32/3.58  330 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_1) # label(axiom).  [assumption].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(330,b,321,b)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(330,b,323,b)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(330,b,324,a)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(330,b,325,a)].
% 3.32/3.58  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(330,b,326,a)].
% 3.38/3.60  331 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom).  [assumption].
% 3.38/3.60  Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(331,b,321,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Ofield(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(331,b,323,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(331,b,324,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(331,b,325,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(331,b,326,a)].
% 3.38/3.60  332 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom).  [assumption].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(332,b,321,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(332,b,323,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(332,b,324,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(332,b,325,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(332,b,326,a)].
% 3.38/3.60  333 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom).  [assumption].
% 3.38/3.60  Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(333,b,321,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(333,b,323,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(333,b,324,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(333,b,325,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(333,b,326,a)].
% 3.38/3.60  334 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom).  [assumption].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(334,b,321,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(334,b,323,b)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(334,b,324,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(334,b,325,a)].
% 3.38/3.60  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(334,b,326,a)].
% 3.38/3.61  335 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom).  [assumption].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(335,b,321,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(335,b,323,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(335,b,324,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(335,b,325,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(335,b,326,a)].
% 3.38/3.61  336 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_0) # label(axiom).  [assumption].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(336,b,321,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(336,b,323,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(336,b,324,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(336,b,325,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(336,b,326,a)].
% 3.38/3.61  337 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_1) # label(axiom).  [assumption].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(337,b,321,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(337,b,323,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(337,b,324,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(337,b,325,a)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(337,b,326,a)].
% 3.38/3.61  338 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom).  [assumption].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(338,b,321,b)].
% 3.38/3.61  Derived: -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(338,b,323,b)].
% 3.38/3.62  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(338,b,324,a)].
% 3.38/3.62  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(338,b,325,a)].
% 3.38/3.62  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(338,b,326,a)].
% 3.38/3.62  339 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom).  [assumption].
% 3.38/3.62  340 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom).  [assumption].
% 3.38/3.62  341 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom).  [assumption].
% 3.38/3.62  342 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom).  [assumption].
% 3.38/3.62  343 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom).  [assumption].
% 3.38/3.62  344 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom).  [assumption].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(344,a,322,a)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(344,a,327,a)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(344,a,328,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(344,a,329,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(344,a,330,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(344,a,331,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(344,a,332,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(344,a,333,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(344,a,334,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(344,a,335,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(344,a,336,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(344,a,337,b)].
% 3.38/3.62  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(344,a,338,b)].
% 3.38/3.62  345 -class_Ring__and__Field_Oring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring_7) # label(axiom).  [assumption].
% 3.38/3.62  Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(345,a,322,a)].
% 3.38/3.62  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(345,a,327,a)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(345,a,328,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(345,a,329,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(345,a,330,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(345,a,331,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(345,a,332,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(345,a,333,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(345,a,334,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(345,a,335,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(345,a,336,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(345,a,337,b)].
% 3.38/3.62  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(345,a,338,b)].
% 3.43/3.65  346 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom).  [assumption].
% 3.43/3.65  347 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom).  [assumption].
% 3.43/3.65  348 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom).  [assumption].
% 3.43/3.65  Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(348,b,321,b)].
% 3.43/3.65  Derived: -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(348,b,323,b)].
% 3.43/3.65  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(348,b,324,a)].
% 3.43/3.65  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(348,b,325,a)].
% 3.43/3.65  Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(348,b,326,a)].
% 3.43/3.65  349 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(37,b,1,a)].
% 3.43/3.65  350 -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(37,b,3,a)].
% 3.43/3.65  351 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(75,b,41,a)].
% 3.43/3.65  352 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(81,b,75,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(352,b,333,b)].
% 3.43/3.65  353 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A).  [resolve(82,b,75,b)].
% 3.43/3.65  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(353,b,333,b)].
% 3.43/3.65  354 -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(160,b,131,b)].
% 3.43/3.65  355 -class_Ring__and__Field_Oring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(160,b,133,b)].
% 3.43/3.65  356 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A).  [resolve(165,a,160,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(356,b,331,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(356,b,332,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(356,b,333,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(356,b,334,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(356,b,335,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(356,b,336,b)].
% 3.43/3.65  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(356,b,338,b)].
% 3.43/3.65  357 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A).  [resolve(166,a,160,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(357,b,331,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(357,b,332,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(357,b,333,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(357,b,334,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(357,b,335,b)].
% 3.43/3.65  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(357,b,336,b)].
% 3.43/3.66  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(357,b,338,b)].
% 3.43/3.66  358 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(236,a,230,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(358,b,331,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(358,b,332,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(358,b,333,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(358,b,334,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(358,b,335,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(358,b,336,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(358,b,337,b)].
% 3.43/3.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(358,b,338,b)].
% 3.43/3.66  359 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A).  [resolve(237,a,230,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(359,b,331,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(359,b,332,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(359,b,333,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(359,b,334,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(359,b,335,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(359,b,336,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(359,b,337,b)].
% 3.43/3.66  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(359,b,338,b)].
% 3.43/3.66  360 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A).  [resolve(241,a,230,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(360,c,331,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(360,c,332,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(360,c,333,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(360,c,334,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(360,c,335,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(360,c,336,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(360,c,337,b)].
% 3.43/3.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(360,c,338,b)].
% 3.43/3.67  361 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A).  [resolve(242,a,230,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(361,c,331,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(361,c,332,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(361,c,333,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(361,c,334,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(361,c,335,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(361,c,336,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(361,c,337,b)].
% 3.43/3.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(361,c,338,b)].
% 3.43/3.67  362 -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0.  [resolve(304,b,280,a)].
% 3.43/3.67  Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(362,a,322,a)].
% 3.43/3.67  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(362,a,327,a)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(362,a,328,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(362,a,329,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(362,a,330,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(362,a,331,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(362,a,332,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(362,a,333,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(362,a,334,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(362,a,335,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(362,a,336,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(362,a,337,b)].
% 3.43/3.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(362,a,338,b)].
% 3.43/3.67  363 -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0.  [resolve(304,b,282,a)].
% 3.43/3.67  Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(363,a,322,a)].
% 3.43/3.67  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(363,a,327,a)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(363,a,328,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(363,a,329,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(363,a,330,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(363,a,331,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(363,a,332,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(363,a,333,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(363,a,334,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(363,a,335,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(363,a,336,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(363,a,337,b)].
% 3.43/3.68  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(363,a,338,b)].
% 3.43/3.68  364 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C).  [resolve(314,a,304,b)].
% 3.43/3.68  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(364,c,322,a)].
% 3.43/3.68  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(364,c,327,a)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(364,c,328,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(364,c,329,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(364,c,330,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(364,c,331,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(364,c,332,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(364,c,333,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(364,c,334,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(364,c,335,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(364,c,336,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(364,c,337,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(364,c,338,b)].
% 3.43/3.68  365 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C).  [resolve(315,a,304,b)].
% 3.43/3.68  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(365,c,322,a)].
% 3.43/3.68  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(365,c,327,a)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(365,c,328,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(365,c,329,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(365,c,330,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(365,c,331,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(365,c,332,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(365,c,333,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(365,c,334,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(365,c,335,b)].
% 3.43/3.68  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(365,c,336,b)].
% 3.54/3.81  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(365,c,337,b)].
% 3.54/3.81  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(365,c,338,b)].
% 3.54/3.81  366 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A).  [resolve(316,a,304,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(366,b,322,a)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(366,b,327,a)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(366,b,328,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(366,b,329,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(366,b,330,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(366,b,331,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(366,b,332,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(366,b,333,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(366,b,334,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(366,b,335,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(366,b,336,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(366,b,337,b)].
% 3.54/3.81  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(366,b,338,b)].
% 3.54/3.81  367 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) # label(axiom).  [assumption].
% 3.54/3.81  368 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_23) # label(axiom).  [assumption].
% 3.54/3.81  369 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom).  [assumption].
% 3.54/3.81  370 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom).  [assumption].
% 3.54/3.81  371 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom).  [assumption].
% 3.54/3.81  372 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom).  [assumption].
% 3.54/3.81  373 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring_18) # label(axiom).  [assumption].
% 3.54/3.81  374 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_4) # label(axiom).  [assumption].
% 3.54/3.81  375 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) # label(axiom).  [assumption].
% 3.54/3.81  376 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) # label(axiom).  [assumption].
% 3.54/3.81  377 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) # label(axiom).  [assumption].
% 3.54/3.81  378 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) # label(axiom).  [assumption].
% 3.54/3.81  379 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) # label(axiom).  [assumption].
% 3.64/3.88  380 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) # label(axiom).  [assumption].
% 3.64/3.88  381 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) # label(axiom).  [assumption].
% 3.64/3.88  382 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_14) # label(axiom).  [assumption].
% 3.64/3.88  383 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_14) # label(axiom).  [assumption].
% 3.64/3.88  384 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_17) # label(axiom).  [assumption].
% 3.64/3.88  385 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_14) # label(axiom).  [assumption].
% 3.64/3.88  386 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_8) # label(axiom).  [assumption].
% 3.64/3.88  387 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_4) # label(axiom).  [assumption].
% 3.64/3.88  388 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(22,b,1,a)].
% 3.64/3.88  389 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(22,b,3,a)].
% 3.64/3.88  390 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A).  [resolve(22,b,10,a)].
% 3.64/3.88  391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(81,b,60,b)].
% 3.64/3.88  392 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(142,b,131,b)].
% 3.64/3.88  393 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(142,b,133,b)].
% 3.64/3.88  394 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(162,a,142,b)].
% 3.64/3.88  395 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(165,a,142,b)].
% 3.64/3.88  396 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(166,a,142,b)].
% 3.64/3.88  397 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(199,b,184,b)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(397,b,368,a)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(397,b,369,a)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(397,b,370,a)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(397,b,371,b)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A).  [resolve(397,b,372,b)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(397,b,373,b)].
% 3.64/3.88  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(397,b,374,b)].
% 3.64/3.88  398 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(200,b,184,b)].
% 3.64/3.88  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(398,b,368,a)].
% 3.64/3.88  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(398,b,369,a)].
% 3.64/3.88  Derived: class_HOL_Oplus(tc_nat).  [resolve(398,b,370,a)].
% 3.64/3.88  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(398,b,371,b)].
% 3.81/4.03  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(398,b,372,b)].
% 3.81/4.03  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(398,b,373,b)].
% 3.81/4.03  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(398,b,374,b)].
% 3.81/4.03  399 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(236,a,212,b)].
% 3.81/4.03  400 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(237,a,212,b)].
% 3.81/4.03  401 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(241,a,212,b)].
% 3.81/4.03  402 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A).  [resolve(242,a,212,b)].
% 3.81/4.03  403 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(289,b,280,a)].
% 3.81/4.03  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(403,a,370,a)].
% 3.81/4.03  Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B).  [resolve(403,a,372,b)].
% 3.81/4.03  404 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(289,b,282,a)].
% 3.81/4.03  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(404,a,370,a)].
% 3.81/4.03  Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B).  [resolve(404,a,372,b)].
% 3.81/4.03  405 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C).  [resolve(314,a,289,b)].
% 3.81/4.03  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(405,c,370,a)].
% 3.81/4.03  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C).  [resolve(405,c,372,b)].
% 3.81/4.03  406 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C).  [resolve(315,a,289,b)].
% 3.81/4.03  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(406,c,370,a)].
% 3.81/4.03  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C).  [resolve(406,c,372,b)].
% 3.81/4.03  407 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_10) # label(axiom).  [assumption].
% 3.81/4.03  408 class_Ring__and__Field_Ocomm__ring(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_24) # label(axiom).  [assumption].
% 3.81/4.03  409 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom).  [assumption].
% 3.81/4.03  410 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom).  [assumption].
% 3.81/4.03  411 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom).  [assumption].
% 3.81/4.03  412 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom).  [assumption].
% 3.81/4.03  413 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring_13) # label(axiom).  [assumption].
% 3.81/4.03  414 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom).  [assumption].
% 3.81/4.03  415 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom).  [assumption].
% 3.81/4.03  416 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom).  [assumption].
% 3.81/4.03  417 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom).  [assumption].
% 3.81/4.03  418 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom).  [assumption].
% 3.81/4.03  419 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_0) # label(axiom).  [assumption].
% 3.84/4.10  420 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom).  [assumption].
% 3.84/4.10  421 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom).  [assumption].
% 3.84/4.10  422 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_4) # label(axiom).  [assumption].
% 3.84/4.10  423 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_1) # label(axiom).  [assumption].
% 3.84/4.10  424 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_0) # label(axiom).  [assumption].
% 3.84/4.10  425 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(20,b,1,a)].
% 3.84/4.10  426 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(20,b,3,a)].
% 3.84/4.10  427 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A).  [resolve(20,b,10,a)].
% 3.84/4.10  428 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(81,b,58,b)].
% 3.84/4.10  429 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(138,b,131,b)].
% 3.84/4.10  430 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(138,b,133,b)].
% 3.84/4.10  431 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(162,a,138,b)].
% 3.84/4.10  432 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(165,a,138,b)].
% 3.84/4.10  433 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(166,a,138,b)].
% 3.84/4.10  434 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(196,a,177,b)].
% 3.84/4.10  435 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(197,a,177,b)].
% 3.84/4.10  436 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(198,b,177,b)].
% 3.84/4.10  437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(199,b,177,b)].
% 3.84/4.10  438 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(200,b,177,b)].
% 3.84/4.10  439 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(201,b,177,b)].
% 3.84/4.10  Derived: class_OrderedGroup_Osemigroup__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(439,b,408,a)].
% 3.84/4.10  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(439,b,409,a)].
% 3.84/4.10  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(439,b,410,b)].
% 3.84/4.10  440 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(202,b,177,b)].
% 3.84/4.10  Derived: class_HOL_Otimes(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(440,b,408,a)].
% 3.84/4.10  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(440,b,409,a)].
% 3.84/4.10  Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(440,b,410,b)].
% 3.84/4.10  441 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(236,a,209,b)].
% 3.84/4.10  442 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(237,a,209,b)].
% 3.84/4.10  443 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(276,b,249,b)].
% 3.84/4.10  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(443,b,408,a)].
% 3.84/4.11  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(443,b,409,a)].
% 3.84/4.11  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(443,b,410,b)].
% 3.84/4.11  444 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(277,b,249,b)].
% 3.84/4.11  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(444,b,408,a)].
% 3.84/4.11  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(444,b,409,a)].
% 3.84/4.11  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(444,b,410,b)].
% 3.84/4.11  445 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(278,c,249,b)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_plus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(445,c,408,a)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(445,c,409,a)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(445,c,410,b)].
% 3.84/4.11  446 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(279,c,249,b)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_plus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_plus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(446,c,408,a)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(446,c,409,a)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(446,c,410,b)].
% 3.84/4.11  447 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(287,b,280,a)].
% 3.84/4.11  448 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(287,b,282,a)].
% 3.84/4.11  449 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(314,a,287,b)].
% 3.84/4.11  450 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(315,a,287,b)].
% 3.84/4.11  451 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(329,b,321,b)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_minus(C,D,tc_fun(A,B)),c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(C,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),c_times(D,c_Numeral_Onumber__of(E,tc_fun(A,B)),tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(451,a,408,a)].
% 3.84/4.11  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(451,a,409,a)].
% 3.84/4.12  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(451,a,410,b)].
% 3.84/4.12  452 -class_Ring__and__Field_Ocomm__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(329,b,323,b)].
% 3.84/4.12  Derived: -class_Numeral_Onumber(tc_fun(A,B)) | c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),c_minus(D,E,tc_fun(A,B)),tc_fun(A,B)) = c_minus(c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),D,tc_fun(A,B)),c_times(c_Numeral_Onumber__of(C,tc_fun(A,B)),E,tc_fun(A,B)),tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(452,a,408,a)].
% 3.84/4.12  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(452,a,409,a)].
% 3.84/4.12  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(452,a,410,b)].
% 3.84/4.12  453 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(329,b,324,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,tc_fun(B,C)),c_uminus(D,tc_fun(B,C)),tc_fun(B,C)) = c_times(A,D,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(453,a,408,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint).  [resolve(453,a,409,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B).  [resolve(453,a,410,b)].
% 3.84/4.12  454 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(329,b,325,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,tc_fun(B,C)),D,tc_fun(B,C)) = c_uminus(c_times(A,D,tc_fun(B,C)),tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(454,a,408,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(454,a,409,a)].
% 3.84/4.12  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B).  [resolve(454,a,410,b)].
% 3.84/4.12  455 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(329,b,326,a)].
% 3.84/4.12  Derived: c_times(A,c_uminus(B,tc_fun(C,D)),tc_fun(C,D)) = c_uminus(c_times(A,B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(455,a,408,a)].
% 3.84/4.12  Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(455,a,409,a)].
% 3.84/4.12  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C).  [resolve(455,a,410,b)].
% 3.84/4.12  456 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(344,a,329,b)].
% 3.84/4.12  Derived: class_OrderedGroup_Oab__group__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(456,b,408,a)].
% 3.84/4.12  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(456,b,409,a)].
% 3.84/4.12  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(456,b,410,b)].
% 3.84/4.12  457 class_HOL_Ominus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(345,a,329,b)].
% 3.84/4.12  Derived: class_HOL_Ominus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(457,b,408,a)].
% 3.84/4.12  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(457,b,409,a)].
% 3.84/4.12  Derived: class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(457,b,410,b)].
% 3.84/4.12  458 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(362,a,329,b)].
% 3.98/4.21  Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(458,b,408,a)].
% 3.98/4.21  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(458,b,409,a)].
% 3.98/4.21  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(458,b,410,b)].
% 3.98/4.21  459 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B).  [resolve(363,a,329,b)].
% 3.98/4.21  Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(459,b,408,a)].
% 3.98/4.21  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(459,b,409,a)].
% 3.98/4.21  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(459,b,410,b)].
% 3.98/4.21  460 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(364,c,329,b)].
% 3.98/4.21  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(A,E,tc_fun(C,D)) | B = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(460,c,408,a)].
% 3.98/4.21  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(460,c,409,a)].
% 3.98/4.21  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(460,c,410,b)].
% 3.98/4.21  461 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C).  [resolve(365,c,329,b)].
% 3.98/4.21  Derived: c_plus(A,B,tc_fun(C,D)) != c_plus(E,B,tc_fun(C,D)) | A = E | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(461,c,408,a)].
% 3.98/4.21  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(461,c,409,a)].
% 3.98/4.21  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(461,c,410,b)].
% 3.98/4.21  462 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(366,b,329,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(462,b,408,a)].
% 3.98/4.21  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(462,b,409,a)].
% 3.98/4.21  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(462,b,410,b)].
% 3.98/4.21  463 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(397,b,373,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(463,b,408,a)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(463,b,409,a)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(463,b,410,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(463,b,420,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(463,b,421,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(463,b,422,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(463,b,423,b)].
% 3.98/4.21  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(463,b,424,b)].
% 3.98/4.21  464 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A).  [resolve(398,b,373,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(464,b,408,a)].
% 3.98/4.21  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(464,b,409,a)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(464,b,410,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(464,b,420,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(464,b,421,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(464,b,422,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(464,b,423,b)].
% 3.98/4.21  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(464,b,424,b)].
% 3.98/4.21  465 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_0 != c_1 # label(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) # label(axiom).  [assumption].
% 3.98/4.21  466 class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_25) # label(axiom).  [assumption].
% 4.23/4.49  Derived: c_0 != c_1 | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(465,a,466,a)].
% 4.23/4.49  467 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_1 != c_0 # label(cls_Ring__and__Field_Oone__neq__zero_0) # label(axiom).  [assumption].
% 4.23/4.49  Derived: c_1 != c_0 | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(467,a,466,a)].
% 4.23/4.49  468 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom).  [assumption].
% 4.23/4.49  Derived: c_0 != c_1.  [resolve(468,a,465,a)].
% 4.23/4.49  Derived: c_1 != c_0.  [resolve(468,a,467,a)].
% 4.23/4.49  469 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom).  [assumption].
% 4.23/4.49  470 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom).  [assumption].
% 4.23/4.49  471 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom).  [assumption].
% 4.23/4.49  472 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) # label(axiom).  [assumption].
% 4.23/4.49  473 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) # label(axiom).  [assumption].
% 4.23/4.49  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(473,a,466,a)].
% 4.23/4.49  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(473,a,471,b)].
% 4.23/4.49  474 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_23) # label(axiom).  [assumption].
% 4.23/4.49  475 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_0) # label(axiom).  [assumption].
% 4.23/4.49  476 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) # label(axiom).  [assumption].
% 4.23/4.49  Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(476,b,473,a)].
% 4.23/4.49  477 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Ofield_11) # label(axiom).  [assumption].
% 4.23/4.49  478 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oidom_11) # label(axiom).  [assumption].
% 4.23/4.49  479 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__field_14) # label(axiom).  [assumption].
% 4.23/4.49  480 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_11) # label(axiom).  [assumption].
% 4.23/4.49  481 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_5) # label(axiom).  [assumption].
% 4.23/4.49  482 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Oring__1_16) # label(axiom).  [assumption].
% 4.23/4.49  483 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Osemiring__1_0) # label(axiom).  [assumption].
% 4.23/4.49  484 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_1) # label(axiom).  [assumption].
% 4.23/4.49  485 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom).  [assumption].
% 4.23/4.49  486 class_Ring__and__Field_Osemiring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_26) # label(axiom).  [assumption].
% 4.23/4.49  487 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom).  [assumption].
% 4.23/4.49  488 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom).  [assumption].
% 4.29/4.51  489 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom).  [assumption].
% 4.29/4.51  490 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom).  [assumption].
% 4.29/4.51  491 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_22) # label(axiom).  [assumption].
% 4.29/4.51  492 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_16) # label(axiom).  [assumption].
% 4.29/4.51  493 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) # label(axiom).  [assumption].
% 4.29/4.51  494 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom).  [assumption].
% 4.29/4.51  495 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom).  [assumption].
% 4.29/4.51  496 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_13) # label(axiom).  [assumption].
% 4.29/4.51  497 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_10) # label(axiom).  [assumption].
% 4.29/4.51  498 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_4) # label(axiom).  [assumption].
% 4.29/4.51  499 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oring__1_15) # label(axiom).  [assumption].
% 4.29/4.51  500 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1_10) # label(axiom).  [assumption].
% 4.29/4.51  501 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom).  [assumption].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(501,a,491,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(501,a,492,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(501,a,494,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(501,a,495,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(501,a,496,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(501,a,497,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(501,a,498,b)].
% 4.29/4.51  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(501,a,499,b)].
% 4.29/4.51  502 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom).  [assumption].
% 4.29/4.51  503 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom).  [assumption].
% 4.29/4.51  504 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom).  [assumption].
% 4.29/4.51  505 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom).  [assumption].
% 4.29/4.51  506 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom).  [assumption].
% 4.29/4.51  507 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_0) # label(axiom).  [assumption].
% 4.29/4.51  508 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B.  [resolve(129,b,108,a)].
% 4.29/4.51  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(508,a,486,a)].
% 4.29/4.51  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(508,a,487,a)].
% 4.43/4.68  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(508,a,488,a)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(508,a,489,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B).  [resolve(508,a,490,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(508,a,491,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(508,a,492,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(508,a,493,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(508,a,494,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(508,a,495,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(508,a,496,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(508,a,497,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(508,a,498,b)].
% 4.43/4.68  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(508,a,499,b)].
% 4.43/4.68  509 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B.  [resolve(129,b,111,a)].
% 4.43/4.68  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(509,a,486,a)].
% 4.43/4.68  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(509,a,487,a)].
% 4.43/4.68  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(509,a,488,a)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(509,a,489,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B).  [resolve(509,a,490,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(509,a,491,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(509,a,492,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(509,a,493,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(509,a,494,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(509,a,495,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(509,a,496,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(509,a,497,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(509,a,498,b)].
% 4.43/4.68  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(509,a,499,b)].
% 4.43/4.68  510 -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(169,b,131,b)].
% 4.43/4.68  511 -class_Ring__and__Field_Osemiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(169,b,133,b)].
% 4.43/4.68  512 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A).  [resolve(169,b,164,a)].
% 4.43/4.68  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(512,a,492,b)].
% 4.43/4.68  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(512,a,507,b)].
% 4.43/4.68  513 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A).  [resolve(239,b,237,a)].
% 4.43/4.68  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(513,a,492,b)].
% 4.43/4.68  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(513,a,493,b)].
% 4.43/4.68  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(513,a,498,b)].
% 4.43/4.68  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(513,a,499,b)].
% 4.43/4.68  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(513,a,507,b)].
% 4.43/4.68  514 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom).  [assumption].
% 4.51/4.73  515 class_Ring__and__Field_Ocomm__semiring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_27) # label(axiom).  [assumption].
% 4.51/4.73  516 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom).  [assumption].
% 4.51/4.73  517 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom).  [assumption].
% 4.51/4.73  518 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom).  [assumption].
% 4.51/4.73  519 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom).  [assumption].
% 4.51/4.73  520 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_20) # label(axiom).  [assumption].
% 4.51/4.73  521 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_10) # label(axiom).  [assumption].
% 4.51/4.73  522 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_11) # label(axiom).  [assumption].
% 4.51/4.73  523 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_12) # label(axiom).  [assumption].
% 4.51/4.73  524 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_13) # label(axiom).  [assumption].
% 4.51/4.73  525 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_14) # label(axiom).  [assumption].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(525,a,515,a)].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint).  [resolve(525,a,516,a)].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat).  [resolve(525,a,517,a)].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(525,a,518,b)].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A).  [resolve(525,a,519,b)].
% 4.51/4.73  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(525,a,520,b)].
% 4.51/4.73  526 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom).  [assumption].
% 4.51/4.73  527 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_8) # label(axiom).  [assumption].
% 4.51/4.73  528 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom).  [assumption].
% 4.51/4.73  529 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) # label(axiom).  [assumption].
% 4.51/4.73  530 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom).  [assumption].
% 4.51/4.73  531 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom).  [assumption].
% 4.51/4.73  532 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_10) # label(axiom).  [assumption].
% 4.51/4.73  533 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_7) # label(axiom).  [assumption].
% 4.51/4.73  534 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oordered__semidom_1) # label(axiom).  [assumption].
% 4.51/4.73  535 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B.  [resolve(121,b,108,a)].
% 4.51/4.73  536 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B.  [resolve(121,b,111,a)].
% 4.58/4.80  537 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(143,b,131,b)].
% 4.58/4.80  538 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(143,b,133,b)].
% 4.58/4.80  539 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(162,a,143,b)].
% 4.58/4.80  540 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(163,a,143,b)].
% 4.58/4.80  541 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(164,a,143,b)].
% 4.58/4.80  542 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(165,a,143,b)].
% 4.58/4.80  543 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(166,a,143,b)].
% 4.58/4.80  544 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(236,a,213,b)].
% 4.58/4.80  545 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(237,a,213,b)].
% 4.58/4.80  546 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(241,a,213,b)].
% 4.58/4.80  547 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(242,a,213,b)].
% 4.58/4.80  548 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(501,a,492,b)].
% 4.58/4.80  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(548,b,515,a)].
% 4.58/4.80  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(548,b,516,a)].
% 4.58/4.80  Derived: class_HOL_Oone(tc_nat).  [resolve(548,b,517,a)].
% 4.58/4.80  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(548,b,518,b)].
% 4.58/4.80  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(548,b,519,b)].
% 4.58/4.80  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(548,b,520,b)].
% 4.58/4.80  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(548,b,529,b)].
% 4.58/4.80  549 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(508,a,492,b)].
% 4.58/4.80  Derived: c_times(c_1,A,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(549,b,515,a)].
% 4.58/4.80  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(549,b,516,a)].
% 4.58/4.80  Derived: c_times(c_1,A,tc_nat) = A.  [resolve(549,b,517,a)].
% 4.58/4.80  Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(549,b,518,b)].
% 4.58/4.80  Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B).  [resolve(549,b,519,b)].
% 4.58/4.80  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(549,b,520,b)].
% 4.58/4.80  550 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B).  [resolve(509,a,492,b)].
% 4.58/4.80  Derived: c_times(A,c_1,tc_fun(B,C)) = A | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(550,b,515,a)].
% 4.58/4.80  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(550,b,516,a)].
% 4.58/4.80  Derived: c_times(A,c_1,tc_nat) = A.  [resolve(550,b,517,a)].
% 4.58/4.80  Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(550,b,518,b)].
% 4.58/4.80  Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B).  [resolve(550,b,519,b)].
% 4.58/4.80  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(550,b,520,b)].
% 4.58/4.80  551 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(512,a,492,b)].
% 4.58/4.80  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(551,b,515,a)].
% 4.58/4.80  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(551,b,516,a)].
% 4.58/4.80  Derived: class_HOL_Oplus(tc_nat).  [resolve(551,b,517,a)].
% 4.58/4.80  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(551,b,518,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(551,b,519,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(551,b,520,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(551,b,529,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(551,b,530,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(551,b,531,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(551,b,532,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(551,b,533,b)].
% 4.71/4.93  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(551,b,534,b)].
% 4.71/4.93  552 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A).  [resolve(513,a,492,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(552,b,515,a)].
% 4.71/4.93  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(552,b,516,a)].
% 4.71/4.93  Derived: class_HOL_Ozero(tc_nat).  [resolve(552,b,517,a)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(552,b,518,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(552,b,519,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(552,b,520,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(552,b,530,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(552,b,531,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(552,b,532,b)].
% 4.71/4.93  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(552,b,533,b)].
% 4.71/4.93  553 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom).  [assumption].
% 4.71/4.93  554 class_Ring__and__Field_Osemiring__1__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_28) # label(axiom).  [assumption].
% 4.71/4.93  555 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom).  [assumption].
% 4.71/4.93  556 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom).  [assumption].
% 4.71/4.93  557 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom).  [assumption].
% 4.71/4.93  558 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom).  [assumption].
% 4.71/4.93  559 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_27) # label(axiom).  [assumption].
% 4.71/4.93  560 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) # label(axiom).  [assumption].
% 4.71/4.93  561 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom).  [assumption].
% 4.71/4.93  562 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom).  [assumption].
% 4.71/4.93  563 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_12) # label(axiom).  [assumption].
% 4.71/4.93  564 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_9) # label(axiom).  [assumption].
% 4.71/4.93  565 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_3) # label(axiom).  [assumption].
% 4.71/4.93  566 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oring__1_19) # label(axiom).  [assumption].
% 4.71/4.93  567 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_11) # label(axiom).  [assumption].
% 4.73/4.98  568 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom).  [assumption].
% 4.73/4.98  569 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_4) # label(axiom).  [assumption].
% 4.73/4.98  570 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom).  [assumption].
% 4.73/4.98  571 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_6) # label(axiom).  [assumption].
% 4.73/4.98  572 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_7) # label(axiom).  [assumption].
% 4.73/4.98  573 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_8) # label(axiom).  [assumption].
% 4.73/4.98  574 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(40,b,1,a)].
% 4.73/4.98  575 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(40,b,3,a)].
% 4.73/4.98  576 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(81,b,78,b)].
% 4.73/4.98  577 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(82,b,78,b)].
% 4.73/4.98  578 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(130,b,108,a)].
% 4.73/4.98  579 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(130,b,111,a)].
% 4.73/4.98  580 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(130,b,116,a)].
% 4.73/4.98  581 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(130,b,117,a)].
% 4.73/4.98  582 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(130,b,118,a)].
% 4.73/4.98  583 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(170,b,131,b)].
% 4.73/4.98  584 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(170,b,133,b)].
% 4.73/4.98  585 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(313,b,280,a)].
% 4.73/4.98  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(585,a,560,b)].
% 4.73/4.98  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(585,a,565,b)].
% 4.73/4.98  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(585,a,566,b)].
% 4.73/4.98  586 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(313,b,282,a)].
% 4.73/4.98  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(586,a,560,b)].
% 4.73/4.98  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(586,a,565,b)].
% 4.73/4.98  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(586,a,566,b)].
% 4.73/4.98  587 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(316,a,313,b)].
% 4.73/4.98  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(587,b,556,a)].
% 4.73/4.98  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(587,b,558,b)].
% 4.73/4.98  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(587,b,560,b)].
% 4.73/4.98  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(587,b,565,b)].
% 4.73/4.98  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(587,b,566,b)].
% 4.97/5.18  588 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(512,a,507,b)].
% 4.97/5.18  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(588,b,566,b)].
% 4.97/5.18  589 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A).  [resolve(513,a,507,b)].
% 4.97/5.18  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(589,b,560,b)].
% 4.97/5.18  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(589,b,565,b)].
% 4.97/5.18  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(589,b,566,b)].
% 4.97/5.18  590 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom).  [assumption].
% 4.97/5.18  591 class_Ring__and__Field_Oring__1(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_29) # label(axiom).  [assumption].
% 4.97/5.18  592 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom).  [assumption].
% 4.97/5.18  593 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom).  [assumption].
% 4.97/5.18  594 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_26) # label(axiom).  [assumption].
% 4.97/5.18  595 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom).  [assumption].
% 4.97/5.18  596 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom).  [assumption].
% 4.97/5.18  597 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oordered__field_5) # label(axiom).  [assumption].
% 4.97/5.18  598 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oordered__idom_2) # label(axiom).  [assumption].
% 4.97/5.18  599 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom).  [assumption].
% 4.97/5.18  600 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom).  [assumption].
% 4.97/5.18  601 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom).  [assumption].
% 4.97/5.18  602 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring__1_13) # label(axiom).  [assumption].
% 4.97/5.18  603 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom).  [assumption].
% 4.97/5.18  604 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom).  [assumption].
% 4.97/5.18  605 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oring__1_2) # label(axiom).  [assumption].
% 4.97/5.18  606 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom).  [assumption].
% 4.97/5.18  607 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom).  [assumption].
% 4.97/5.18  608 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(38,b,1,a)].
% 4.97/5.18  609 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(38,b,3,a)].
% 4.97/5.18  610 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(38,b,9,a)].
% 4.97/5.18  611 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A).  [resolve(38,b,10,a)].
% 4.97/5.18  612 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(76,b,41,a)].
% 4.97/5.18  613 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B.  [resolve(128,b,108,a)].
% 4.97/5.18  614 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B.  [resolve(128,b,111,a)].
% 4.97/5.18  615 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(161,b,131,b)].
% 4.99/5.22  616 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(161,b,133,b)].
% 4.99/5.22  617 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(165,a,161,b)].
% 4.99/5.22  618 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(166,a,161,b)].
% 4.99/5.22  619 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(236,a,231,b)].
% 4.99/5.22  620 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(237,a,231,b)].
% 4.99/5.22  621 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A).  [resolve(241,a,231,b)].
% 4.99/5.22  622 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A).  [resolve(242,a,231,b)].
% 4.99/5.22  623 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0.  [resolve(305,b,280,a)].
% 4.99/5.22  624 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0.  [resolve(305,b,282,a)].
% 4.99/5.22  625 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C).  [resolve(314,a,305,b)].
% 4.99/5.22  626 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C).  [resolve(315,a,305,b)].
% 4.99/5.22  627 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(316,a,305,b)].
% 4.99/5.22  628 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(317,a,305,b)].
% 4.99/5.22  629 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(318,a,305,b)].
% 4.99/5.22  630 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(348,b,321,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(630,a,594,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(630,a,595,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(630,a,596,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(630,a,597,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(630,a,598,b)].
% 4.99/5.22  631 -class_Ring__and__Field_Oring__1(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(348,b,323,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(631,a,594,b)].
% 4.99/5.22  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(631,a,595,b)].
% 5.02/5.24  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(631,a,596,b)].
% 5.02/5.24  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(631,a,597,b)].
% 5.02/5.24  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(631,a,598,b)].
% 5.02/5.24  632 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(348,b,324,a)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(632,a,594,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B).  [resolve(632,a,595,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B).  [resolve(632,a,596,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(632,a,597,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(632,a,598,b)].
% 5.02/5.24  633 -class_Ring__and__Field_Oring__1(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(348,b,325,a)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(633,a,594,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B).  [resolve(633,a,595,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B).  [resolve(633,a,596,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(633,a,597,b)].
% 5.02/5.24  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(633,a,598,b)].
% 5.02/5.24  634 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(348,b,326,a)].
% 5.02/5.24  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(634,a,594,b)].
% 5.02/5.24  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C).  [resolve(634,a,595,b)].
% 5.02/5.24  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C).  [resolve(634,a,596,b)].
% 5.02/5.24  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(634,a,597,b)].
% 5.02/5.24  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(634,a,598,b)].
% 5.02/5.24  635 class_HOL_Oone(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(501,a,499,b)].
% 5.02/5.24  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(635,b,595,b)].
% 5.02/5.24  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(635,b,596,b)].
% 5.02/5.24  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(635,b,597,b)].
% 5.02/5.24  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(635,b,598,b)].
% 5.02/5.24  636 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(508,a,499,b)].
% 5.02/5.24  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(636,b,595,b)].
% 5.02/5.24  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(636,b,596,b)].
% 5.02/5.24  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(636,b,597,b)].
% 5.02/5.24  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(636,b,598,b)].
% 5.02/5.25  637 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B).  [resolve(509,a,499,b)].
% 5.02/5.25  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(637,b,595,b)].
% 5.02/5.25  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(637,b,596,b)].
% 5.02/5.25  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(637,b,597,b)].
% 5.02/5.25  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(637,b,598,b)].
% 5.02/5.25  638 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(513,a,499,b)].
% 5.02/5.25  639 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(585,a,566,b)].
% 5.02/5.25  Derived: c_times(c_0,A,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(639,b,591,a)].
% 5.02/5.25  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(639,b,592,a)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(639,b,593,b)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(639,b,594,b)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(639,b,595,b)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(639,b,596,b)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(639,b,597,b)].
% 5.02/5.25  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(639,b,598,b)].
% 5.02/5.25  640 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B).  [resolve(586,a,566,b)].
% 5.02/5.25  Derived: c_times(A,c_0,tc_fun(B,C)) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(640,b,591,a)].
% 5.02/5.25  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(640,b,592,a)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(640,b,593,b)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(640,b,594,b)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(640,b,595,b)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(640,b,596,b)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(640,b,597,b)].
% 5.02/5.25  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(640,b,598,b)].
% 5.02/5.25  641 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(587,b,566,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(641,b,591,a)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(641,b,592,a)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(641,b,593,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(641,b,594,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(641,b,595,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(641,b,596,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(641,b,597,b)].
% 5.02/5.25  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(641,b,598,b)].
% 5.02/5.25  642 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(588,b,566,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(642,b,591,a)].
% 5.02/5.25  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(642,b,592,a)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(642,b,593,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(642,b,594,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(642,b,595,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(642,b,596,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(642,b,597,b)].
% 5.02/5.25  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(642,b,598,b)].
% 5.02/5.30  643 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A).  [resolve(589,b,566,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(643,b,591,a)].
% 5.02/5.30  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(643,b,592,a)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(643,b,593,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(643,b,594,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(643,b,595,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(643,b,596,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(643,b,597,b)].
% 5.02/5.30  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(643,b,598,b)].
% 5.02/5.30  644 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_0,c_IntDef_ONats,A) # label(cls_IntDef_ONats__0_0) # label(axiom).  [assumption].
% 5.02/5.30  645 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B) # label(clsarity_fun_30) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_in(c_0,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(644,a,645,a)].
% 5.02/5.30  646 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_1,c_IntDef_ONats,A) # label(cls_IntDef_ONats__1_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_in(c_1,c_IntDef_ONats,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(646,a,645,a)].
% 5.02/5.30  647 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__add_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: -c_in(A,c_IntDef_ONats,tc_fun(B,C)) | -c_in(D,c_IntDef_ONats,tc_fun(B,C)) | c_in(c_plus(D,A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(647,a,645,a)].
% 5.02/5.30  648 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__mult_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: -c_in(A,c_IntDef_ONats,tc_fun(B,C)) | -c_in(D,c_IntDef_ONats,tc_fun(B,C)) | c_in(c_times(D,A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(648,a,645,a)].
% 5.02/5.30  649 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A) # label(cls_IntDef_Oof__nat__in__Nats_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_in(c_NatArith_Oof__nat(A,tc_fun(B,C)),c_IntDef_ONats,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(649,a,645,a)].
% 5.02/5.30  650 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A) # label(cls_NatArith_Oof__nat_Oof__nat__Suc_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_NatArith_Oof__nat(c_Suc(A),tc_fun(B,C)) = c_plus(c_NatArith_Oof__nat(A,tc_fun(B,C)),c_1,tc_fun(B,C)) | -class_Ring__and__Field_Ocomm__ring__1(C).  [resolve(650,a,645,a)].
% 5.02/5.30  651 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_1,A) = c_1 # label(cls_NatArith_Oof__nat__1_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_NatArith_Oof__nat(c_1,tc_fun(A,B)) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(651,a,645,a)].
% 5.02/5.30  652 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__add_0) # label(axiom).  [assumption].
% 5.02/5.30  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_fun(C,D)) = c_plus(c_NatArith_Oof__nat(A,tc_fun(C,D)),c_NatArith_Oof__nat(B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(652,a,645,a)].
% 5.02/5.30  653 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__mult_0) # label(axiom).  [assumption].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_fun(C,D)) = c_times(c_NatArith_Oof__nat(A,tc_fun(C,D)),c_NatArith_Oof__nat(B,tc_fun(C,D)),tc_fun(C,D)) | -class_Ring__and__Field_Ocomm__ring__1(D).  [resolve(653,a,645,a)].
% 5.11/5.35  654 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_IntDef_Oiszero(c_1,A) # label(cls_Numeral_Obin__rel__simps__10_0) # label(axiom).  [assumption].
% 5.11/5.35  Derived: -c_IntDef_Oiszero(c_1,tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(654,a,645,a)].
% 5.11/5.35  655 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom).  [assumption].
% 5.11/5.35  Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,644,a)].
% 5.11/5.35  Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,646,a)].
% 5.11/5.35  Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,647,a)].
% 5.11/5.35  Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,648,a)].
% 5.11/5.35  Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(655,a,649,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint).  [resolve(655,a,650,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1.  [resolve(655,a,651,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(655,a,652,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(655,a,653,a)].
% 5.11/5.35  Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint).  [resolve(655,a,654,a)].
% 5.11/5.35  656 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom).  [assumption].
% 5.11/5.35  Derived: c_in(c_0,c_IntDef_ONats,tc_nat).  [resolve(656,a,644,a)].
% 5.11/5.35  Derived: c_in(c_1,c_IntDef_ONats,tc_nat).  [resolve(656,a,646,a)].
% 5.11/5.35  Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(656,a,647,a)].
% 5.11/5.35  Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(656,a,648,a)].
% 5.11/5.35  Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(656,a,649,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat).  [resolve(656,a,650,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1.  [resolve(656,a,651,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(656,a,652,a)].
% 5.11/5.35  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(656,a,653,a)].
% 5.11/5.35  Derived: -c_IntDef_Oiszero(c_1,tc_nat).  [resolve(656,a,654,a)].
% 5.11/5.35  657 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom).  [assumption].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(657,b,644,a)].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(657,b,646,a)].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(657,b,647,a)].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(657,b,648,a)].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(657,b,649,a)].
% 5.11/5.35  Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(657,b,650,a)].
% 5.11/5.37  Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(657,b,651,a)].
% 5.11/5.37  Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(657,b,652,a)].
% 5.11/5.37  Derived: -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(657,b,653,a)].
% 5.11/5.37  Derived: -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(657,b,654,a)].
% 5.11/5.37  658 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom).  [assumption].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(658,b,644,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(658,b,646,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(658,b,647,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(658,b,648,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(658,b,649,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(658,b,650,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(658,b,651,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(658,b,652,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(658,b,653,a)].
% 5.11/5.37  Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(658,b,654,a)].
% 5.11/5.37  659 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_28) # label(axiom).  [assumption].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(659,b,644,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(659,b,646,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(659,b,647,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(659,b,648,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(659,b,649,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(659,b,650,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(659,b,651,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(659,b,652,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(659,b,653,a)].
% 5.11/5.37  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(659,b,654,a)].
% 5.11/5.37  660 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) # label(axiom).  [assumption].
% 5.11/5.37  661 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) # label(axiom).  [assumption].
% 5.11/5.37  662 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) # label(axiom).  [assumption].
% 5.11/5.38  663 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) # label(axiom).  [assumption].
% 5.11/5.38  664 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) # label(axiom).  [assumption].
% 5.11/5.38  665 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) # label(axiom).  [assumption].
% 5.11/5.38  666 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) # label(axiom).  [assumption].
% 5.11/5.38  667 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) # label(axiom).  [assumption].
% 5.11/5.38  668 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) # label(axiom).  [assumption].
% 5.11/5.38  669 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_6) # label(axiom).  [assumption].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(669,b,644,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(669,b,646,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(669,b,647,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(669,b,648,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(669,b,649,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(669,b,650,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(669,b,651,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(669,b,652,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(669,b,653,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(669,b,654,a)].
% 5.11/5.38  670 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_6) # label(axiom).  [assumption].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(670,b,644,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(670,b,646,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(670,b,647,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(670,b,648,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(670,b,649,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(670,b,650,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(670,b,651,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(670,b,652,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(670,b,653,a)].
% 5.11/5.38  Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(670,b,654,a)].
% 5.11/5.39  671 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__field_9) # label(axiom).  [assumption].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(671,b,644,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(671,b,646,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(671,b,647,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(671,b,648,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(671,b,649,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(671,b,650,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(671,b,651,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(671,b,652,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(671,b,653,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(671,b,654,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A).  [resolve(671,b,667,a)].
% 5.11/5.39  672 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__idom_6) # label(axiom).  [assumption].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(672,b,644,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(672,b,646,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(672,b,647,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(672,b,648,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(672,b,649,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(672,b,650,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(672,b,651,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(672,b,652,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(672,b,653,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(672,b,654,a)].
% 5.11/5.39  673 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oordered__semidom_0) # label(axiom).  [assumption].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(673,b,644,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(673,b,646,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(673,b,647,a)].
% 5.11/5.39  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(673,b,648,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(673,b,649,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(673,b,650,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(673,b,651,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(673,b,652,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(673,b,653,a)].
% 5.19/5.43  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(673,b,654,a)].
% 5.19/5.43  674 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(23,b,1,a)].
% 5.19/5.43  675 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(23,b,3,a)].
% 5.19/5.43  676 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(23,b,9,a)].
% 5.19/5.43  677 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A).  [resolve(23,b,10,a)].
% 5.19/5.43  678 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(61,b,41,a)].
% 5.19/5.43  679 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(98,b,83,a)].
% 5.19/5.43  680 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Otimes(A).  [resolve(98,b,89,a)].
% 5.19/5.43  681 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_1,B,A) = B.  [resolve(122,b,108,a)].
% 5.19/5.43  682 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_1,A) = B.  [resolve(122,b,111,a)].
% 5.19/5.43  683 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(144,b,131,b)].
% 5.19/5.43  684 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(144,b,133,b)].
% 5.19/5.43  685 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(198,b,186,b)].
% 5.19/5.43  686 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(199,b,186,b)].
% 5.19/5.43  687 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(200,b,186,b)].
% 5.19/5.43  688 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(201,b,186,b)].
% 5.19/5.43  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(688,b,656,a)].
% 5.19/5.43  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A).  [resolve(688,b,658,b)].
% 5.19/5.43  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(688,b,659,b)].
% 5.19/5.43  689 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(202,b,186,b)].
% 5.19/5.43  Derived: class_HOL_Otimes(tc_nat).  [resolve(689,b,656,a)].
% 5.19/5.43  Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A).  [resolve(689,b,658,b)].
% 5.19/5.43  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(689,b,659,b)].
% 5.19/5.43  690 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(236,a,214,b)].
% 5.19/5.43  691 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(237,a,214,b)].
% 5.19/5.43  692 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(241,a,214,b)].
% 5.33/5.60  693 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(242,a,214,b)].
% 5.33/5.60  694 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(c_0,B,A) = c_0.  [resolve(290,b,280,a)].
% 5.33/5.60  695 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_times(B,c_0,A) = c_0.  [resolve(290,b,282,a)].
% 5.33/5.60  696 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C).  [resolve(314,a,290,b)].
% 5.33/5.60  697 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__1__cancel(C).  [resolve(315,a,290,b)].
% 5.33/5.60  698 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A).  [resolve(476,b,473,a)].
% 5.33/5.60  699 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(508,a,493,b)].
% 5.33/5.60  700 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(509,a,493,b)].
% 5.33/5.60  701 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(513,a,493,b)].
% 5.33/5.60  702 class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(548,b,529,b)].
% 5.33/5.60  Derived: class_HOL_Oone(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(702,b,645,a)].
% 5.33/5.60  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(702,b,655,a)].
% 5.33/5.60  Derived: class_HOL_Oone(tc_nat).  [resolve(702,b,656,a)].
% 5.33/5.60  Derived: class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(702,b,657,b)].
% 5.33/5.60  Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A).  [resolve(702,b,658,b)].
% 5.33/5.60  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(702,b,659,b)].
% 5.33/5.60  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(702,b,673,b)].
% 5.33/5.60  703 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(551,b,529,b)].
% 5.33/5.60  Derived: class_HOL_Oplus(tc_nat).  [resolve(703,b,656,a)].
% 5.33/5.60  Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A).  [resolve(703,b,658,b)].
% 5.33/5.60  704 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(585,a,560,b)].
% 5.33/5.60  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(704,b,656,a)].
% 5.33/5.60  Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B).  [resolve(704,b,658,b)].
% 5.33/5.60  705 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B).  [resolve(586,a,560,b)].
% 5.33/5.60  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(705,b,656,a)].
% 5.33/5.60  Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B).  [resolve(705,b,658,b)].
% 5.33/5.60  706 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(587,b,560,b)].
% 5.33/5.60  Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(706,b,656,a)].
% 5.33/5.60  Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(706,b,658,b)].
% 5.33/5.60  707 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A).  [resolve(589,b,560,b)].
% 5.33/5.60  Derived: class_HOL_Ozero(tc_nat).  [resolve(707,b,656,a)].
% 5.33/5.60  Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A).  [resolve(707,b,658,b)].
% 5.33/5.60  708 -class_OrderedGroup_Oab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_0) # label(axiom).  [assumption].
% 5.33/5.60  709 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B) # label(clsarity_fun_8) # label(axiom).  [assumption].
% 5.33/5.60  710 class_OrderedGroup_Oab__semigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_set_11) # label(axiom).  [assumption].
% 5.33/5.60  711 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_7) # label(axiom).  [assumption].
% 5.33/5.60  712 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat_15) # label(axiom).  [assumption].
% 5.33/5.60  713 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom).  [assumption].
% 5.33/5.60  714 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom).  [assumption].
% 5.33/5.62  Derived: class_OrderedGroup_Osemigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B).  [resolve(708,a,709,a)].
% 5.33/5.62  Derived: class_OrderedGroup_Osemigroup__add(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(708,a,710,a)].
% 5.33/5.62  715 -class_OrderedGroup_Oab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__semigroup__add_1) # label(axiom).  [assumption].
% 5.33/5.62  Derived: class_HOL_Oplus(tc_fun(A,B)) | -class_OrderedGroup_Ocomm__monoid__add(B).  [resolve(715,a,709,a)].
% 5.33/5.62  Derived: class_HOL_Oplus(tc_set(A)) | -class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(715,a,710,a)].
% 5.33/5.62  716 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom).  [assumption].
% 5.33/5.62  717 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom).  [assumption].
% 5.33/5.62  718 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom).  [assumption].
% 5.33/5.62  719 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom).  [assumption].
% 5.33/5.62  720 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom).  [assumption].
% 5.33/5.62  721 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) # label(axiom).  [assumption].
% 5.33/5.62  722 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom).  [assumption].
% 5.33/5.62  723 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom).  [assumption].
% 5.33/5.62  724 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) # label(axiom).  [assumption].
% 5.33/5.62  725 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) # label(axiom).  [assumption].
% 5.33/5.62  726 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom).  [assumption].
% 5.33/5.62  727 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_16) # label(axiom).  [assumption].
% 5.33/5.62  728 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_26) # label(axiom).  [assumption].
% 5.33/5.62  729 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom).  [assumption].
% 5.33/5.62  730 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom).  [assumption].
% 5.33/5.62  731 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) # label(axiom).  [assumption].
% 5.33/5.62  732 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_27) # label(axiom).  [assumption].
% 5.33/5.62  733 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom).  [assumption].
% 5.33/5.62  734 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_11) # label(axiom).  [assumption].
% 5.43/5.65  735 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom).  [assumption].
% 5.43/5.65  736 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_5) # label(axiom).  [assumption].
% 5.43/5.65  737 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) # label(axiom).  [assumption].
% 5.43/5.65  738 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_8) # label(axiom).  [assumption].
% 5.43/5.65  739 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_16) # label(axiom).  [assumption].
% 5.43/5.65  740 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_8) # label(axiom).  [assumption].
% 5.43/5.65  741 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom).  [assumption].
% 5.43/5.65  742 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom).  [assumption].
% 5.43/5.65  743 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_OrderedGroup_Oab__group__add(B).  [resolve(41,a,42,a)].
% 5.43/5.65  744 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(41,a,43,a)].
% 5.43/5.65  745 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(41,a,44,a)].
% 5.43/5.65  746 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(41,a,45,b)].
% 5.43/5.65  747 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A).  [resolve(41,a,46,b)].
% 5.43/5.65  748 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(50,b,41,a)].
% 5.43/5.65  749 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(56,b,41,a)].
% 5.43/5.65  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(749,b,708,a)].
% 5.43/5.65  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(749,b,715,a)].
% 5.43/5.65  750 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(68,b,41,a)].
% 5.43/5.65  751 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(71,b,41,a)].
% 5.43/5.65  752 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A).  [resolve(74,b,41,a)].
% 5.43/5.65  753 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(162,a,132,a)].
% 5.43/5.65  754 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(162,a,137,b)].
% 5.43/5.65  755 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(162,a,139,b)].
% 5.43/5.65  756 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(162,a,145,b)].
% 5.43/5.65  757 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(162,a,146,b)].
% 5.43/5.65  758 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(162,a,147,b)].
% 5.43/5.65  759 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(162,a,148,b)].
% 5.43/5.65  760 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(162,a,149,b)].
% 5.43/5.65  761 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(162,a,150,b)].
% 5.43/5.65  762 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(162,a,152,b)].
% 5.43/5.69  763 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(162,a,153,b)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(763,a,708,a)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(763,a,715,a)].
% 5.43/5.69  764 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(162,a,155,b)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(764,a,708,a)].
% 5.43/5.69  765 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(162,a,156,b)].
% 5.43/5.69  766 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(162,a,157,b)].
% 5.43/5.69  767 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(162,a,159,b)].
% 5.43/5.69  768 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(198,b,172,a)].
% 5.43/5.69  769 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(198,b,173,a)].
% 5.43/5.69  770 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(198,b,174,a)].
% 5.43/5.69  771 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(198,b,175,b)].
% 5.43/5.69  772 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(198,b,176,b)].
% 5.43/5.69  773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(198,b,178,b)].
% 5.43/5.69  774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(198,b,193,b)].
% 5.43/5.69  775 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(316,a,297,b)].
% 5.43/5.69  776 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(316,a,303,b)].
% 5.43/5.69  777 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(366,b,322,a)].
% 5.43/5.69  778 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(366,b,327,a)].
% 5.43/5.69  779 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(366,b,328,b)].
% 5.43/5.69  780 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(366,b,330,b)].
% 5.43/5.69  781 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(366,b,331,b)].
% 5.43/5.69  782 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(366,b,332,b)].
% 5.43/5.69  783 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(366,b,333,b)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(783,a,708,a)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A).  [resolve(783,a,715,a)].
% 5.43/5.69  784 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(366,b,334,b)].
% 5.43/5.69  785 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(366,b,335,b)].
% 5.43/5.69  786 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(366,b,336,b)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(786,a,708,a)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(786,a,715,a)].
% 5.43/5.69  787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(366,b,337,b)].
% 5.43/5.69  788 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(366,b,338,b)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(788,a,708,a)].
% 5.43/5.69  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(788,a,715,a)].
% 5.43/5.69  789 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(462,b,408,a)].
% 5.58/5.81  790 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(462,b,409,a)].
% 5.58/5.81  791 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(462,b,410,b)].
% 5.58/5.81  792 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(587,b,556,a)].
% 5.58/5.81  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(792,a,708,a)].
% 5.58/5.81  793 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(587,b,558,b)].
% 5.58/5.81  Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(793,a,708,a)].
% 5.58/5.81  794 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(587,b,565,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(794,a,708,a)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A).  [resolve(794,a,715,a)].
% 5.58/5.81  795 class_OrderedGroup_Oab__semigroup__add(tc_fun(A,B)) | -class_Ring__and__Field_Ocomm__ring__1(B).  [resolve(641,b,591,a)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(tc_fun(B,A)).  [resolve(795,a,708,a)].
% 5.58/5.81  796 class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint).  [resolve(641,b,592,a)].
% 5.58/5.81  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(796,a,708,a)].
% 5.58/5.81  797 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(641,b,593,b)].
% 5.58/5.81  Derived: -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(797,a,708,a)].
% 5.58/5.81  798 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(641,b,594,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(798,a,708,a)].
% 5.58/5.81  799 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(641,b,595,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(799,a,708,a)].
% 5.58/5.81  800 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(641,b,596,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(800,a,708,a)].
% 5.58/5.81  801 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(641,b,597,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(801,a,708,a)].
% 5.58/5.81  802 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(641,b,598,b)].
% 5.58/5.81  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(802,a,708,a)].
% 5.58/5.81  803 class_OrderedGroup_Oab__semigroup__add(tc_nat).  [resolve(706,b,656,a)].
% 5.58/5.81  Derived: class_HOL_Oplus(tc_nat).  [resolve(803,a,715,a)].
% 5.58/5.81  804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A).  [resolve(706,b,658,b)].
% 5.58/5.81  Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A).  [resolve(804,a,715,a)].
% 5.58/5.81  805 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom).  [assumption].
% 5.58/5.81  806 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset # label(cls_Finite__Set_OMax__ge_0) # label(axiom).  [assumption].
% 5.58/5.81  807 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMax__in_0) # label(axiom).  [assumption].
% 5.58/5.81  808 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A) # label(cls_Finite__Set_OMax__insert_0) # label(axiom).  [assumption].
% 5.58/5.81  809 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__le__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  810 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  811 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_2) # label(axiom).  [assumption].
% 5.58/5.81  812 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__less__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  813 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  814 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_2) # label(axiom).  [assumption].
% 5.58/5.81  815 -class_Orderings_Olinorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMax__singleton_0) # label(axiom).  [assumption].
% 5.58/5.81  816 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  817 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  818 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_2) # label(axiom).  [assumption].
% 5.58/5.81  819 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  820 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  821 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_2) # label(axiom).  [assumption].
% 5.58/5.81  822 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMin__in_0) # label(axiom).  [assumption].
% 5.58/5.81  823 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A) # label(cls_Finite__Set_OMin__insert_0) # label(axiom).  [assumption].
% 5.58/5.81  824 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__le_0) # label(axiom).  [assumption].
% 5.58/5.81  825 -class_Orderings_Olinorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMin__singleton_0) # label(axiom).  [assumption].
% 5.58/5.81  826 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) # label(axiom).  [assumption].
% 5.58/5.81  827 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) # label(axiom).  [assumption].
% 5.58/5.81  828 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) # label(axiom).  [assumption].
% 5.58/5.81  829 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) # label(axiom).  [assumption].
% 5.58/5.81  830 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) # label(axiom).  [assumption].
% 5.58/5.81  831 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A) # label(cls_Orderings_Omax__less__iff__conj_0) # label(axiom).  [assumption].
% 5.58/5.81  832 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A) # label(cls_Orderings_Omax__less__iff__conj_1) # label(axiom).  [assumption].
% 5.58/5.81  833 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omax__less__iff__conj_2) # label(axiom).  [assumption].
% 5.58/5.81  834 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A) # label(cls_Orderings_Omin__less__iff__conj_0) # label(axiom).  [assumption].
% 5.58/5.81  835 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A) # label(cls_Orderings_Omin__less__iff__conj_1) # label(axiom).  [assumption].
% 5.58/5.81  836 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__less__iff__conj_2) # label(axiom).  [assumption].
% 5.58/5.81  837 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) # label(axiom).  [assumption].
% 5.58/5.81  838 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) # label(axiom).  [assumption].
% 5.58/5.81  839 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) # label(axiom).  [assumption].
% 5.58/5.81  840 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom).  [assumption].
% 5.58/5.81  841 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) # label(axiom).  [assumption].
% 5.58/5.81  842 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) # label(axiom).  [assumption].
% 5.58/5.81  843 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) # label(axiom).  [assumption].
% 5.58/5.81  844 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) # label(axiom).  [assumption].
% 5.58/5.81  845 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom).  [assumption].
% 5.58/5.81  846 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) # label(axiom).  [assumption].
% 5.58/5.81  847 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A) # label(cls_SetInterval_OCompl__atLeast_0) # label(axiom).  [assumption].
% 5.58/5.81  848 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A) # label(cls_SetInterval_OCompl__atMost_0) # label(axiom).  [assumption].
% 5.58/5.81  849 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A) # label(cls_SetInterval_OCompl__greaterThan_0) # label(axiom).  [assumption].
% 5.58/5.81  850 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A) # label(cls_SetInterval_OCompl__lessThan_0) # label(axiom).  [assumption].
% 5.58/5.81  851 -class_Orderings_Olinorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C # label(cls_SetInterval_OatLeast__eq__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  852 -class_Orderings_Olinorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C # label(cls_SetInterval_OatMost__eq__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  853 -class_Orderings_Olinorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C # label(cls_SetInterval_OgreaterThan__eq__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  854 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OgreaterThan__subset__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  855 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)) # label(cls_SetInterval_OgreaterThan__subset__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  856 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A) # label(cls_SetInterval_Oivl__diff_0) # label(axiom).  [assumption].
% 5.58/5.81  857 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_0) # label(axiom).  [assumption].
% 5.58/5.81  858 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_1) # label(axiom).  [assumption].
% 5.58/5.81  859 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_2) # label(axiom).  [assumption].
% 5.58/5.81  860 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_3) # label(axiom).  [assumption].
% 5.58/5.81  861 -class_Orderings_Olinorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C # label(cls_SetInterval_OlessThan__eq__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  862 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OlessThan__subset__iff_0) # label(axiom).  [assumption].
% 5.58/5.81  863 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) # label(cls_SetInterval_OlessThan__subset__iff_1) # label(axiom).  [assumption].
% 5.58/5.81  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,806,a)].
% 5.58/5.81  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,807,a)].
% 5.58/5.81  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(805,a,808,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,809,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,810,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,811,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,812,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,813,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,814,a)].
% 5.58/5.82  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,815,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,816,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,817,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,818,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,819,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,820,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,821,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,822,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(805,a,823,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(805,a,824,a)].
% 5.58/5.82  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,825,a)].
% 5.58/5.82  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(805,a,826,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,827,a)].
% 5.58/5.82  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(805,a,828,a)].
% 5.58/5.82  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint).  [resolve(805,a,829,b)].
% 5.58/5.82  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(805,a,830,b)].
% 5.58/5.82  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(805,a,831,a)].
% 5.58/5.82  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(805,a,832,a)].
% 5.58/5.82  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(805,a,833,a)].
% 5.58/5.82  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(805,a,834,a)].
% 5.58/5.82  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(805,a,835,a)].
% 5.58/5.82  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(805,a,836,a)].
% 5.58/5.82  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(805,a,837,a)].
% 5.58/5.82  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(805,a,838,a)].
% 5.58/5.82  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(805,a,839,a)].
% 5.58/5.82  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(805,a,840,a)].
% 5.58/5.82  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint).  [resolve(805,a,841,a)].
% 5.58/5.82  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(805,a,842,a)].
% 5.58/5.82  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(805,a,843,a)].
% 5.58/5.82  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(805,a,844,a)].
% 5.58/5.82  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(805,a,845,a)].
% 5.58/5.82  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint).  [resolve(805,a,846,a)].
% 5.58/5.82  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint).  [resolve(805,a,847,a)].
% 5.58/5.82  Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint).  [resolve(805,a,848,a)].
% 5.58/5.82  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint).  [resolve(805,a,849,a)].
% 5.58/5.82  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint).  [resolve(805,a,850,a)].
% 5.58/5.82  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,851,a)].
% 5.58/5.82  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,852,a)].
% 5.58/5.82  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,853,a)].
% 5.58/5.82  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(805,a,854,a)].
% 5.58/5.82  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(805,a,855,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint).  [resolve(805,a,856,a)].
% 5.58/5.83  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(805,a,857,a)].
% 5.58/5.83  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(805,a,858,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(805,a,859,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(805,a,860,a)].
% 5.58/5.83  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(805,a,861,a)].
% 5.58/5.83  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(805,a,862,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(805,a,863,a)].
% 5.58/5.83  864 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom).  [assumption].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset.  [resolve(864,a,806,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(864,a,807,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat).  [resolve(864,a,808,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset.  [resolve(864,a,809,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(864,a,810,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(864,a,811,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset.  [resolve(864,a,812,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(864,a,813,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(864,a,814,a)].
% 5.58/5.83  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(864,a,815,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset.  [resolve(864,a,816,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(864,a,817,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(864,a,818,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset.  [resolve(864,a,819,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(864,a,820,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(864,a,821,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(864,a,822,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat).  [resolve(864,a,823,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset.  [resolve(864,a,824,a)].
% 5.58/5.83  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(864,a,825,a)].
% 5.58/5.83  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(864,a,826,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A.  [resolve(864,a,827,a)].
% 5.58/5.83  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A.  [resolve(864,a,828,a)].
% 5.58/5.83  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat).  [resolve(864,a,829,b)].
% 5.58/5.83  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat).  [resolve(864,a,830,b)].
% 5.58/5.83  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(864,a,831,a)].
% 5.58/5.83  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(864,a,832,a)].
% 5.58/5.83  Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(864,a,833,a)].
% 5.58/5.83  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(864,a,834,a)].
% 5.58/5.83  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(864,a,835,a)].
% 5.58/5.83  Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(864,a,836,a)].
% 5.58/5.83  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(864,a,837,a)].
% 5.58/5.83  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(864,a,838,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(864,a,839,a)].
% 5.58/5.83  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(864,a,840,a)].
% 5.58/5.83  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat).  [resolve(864,a,841,a)].
% 5.58/5.83  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(864,a,842,a)].
% 5.58/5.83  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(864,a,843,a)].
% 5.58/5.83  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(864,a,844,a)].
% 5.58/5.83  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(864,a,845,a)].
% 5.58/5.83  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat).  [resolve(864,a,846,a)].
% 5.58/5.85  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(864,a,847,a)].
% 5.58/5.85  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(864,a,848,a)].
% 5.58/5.85  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(864,a,849,a)].
% 5.58/5.85  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(864,a,850,a)].
% 5.58/5.85  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(864,a,851,a)].
% 5.58/5.85  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(864,a,852,a)].
% 5.58/5.85  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(864,a,853,a)].
% 5.58/5.85  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(864,a,854,a)].
% 5.58/5.85  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)).  [resolve(864,a,855,a)].
% 5.58/5.85  Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat).  [resolve(864,a,856,a)].
% 5.58/5.85  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(864,a,857,a)].
% 5.58/5.85  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(864,a,858,a)].
% 5.58/5.85  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)).  [resolve(864,a,859,a)].
% 5.58/5.85  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)).  [resolve(864,a,860,a)].
% 5.58/5.85  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(864,a,861,a)].
% 5.58/5.85  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(864,a,862,a)].
% 5.58/5.85  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)).  [resolve(864,a,863,a)].
% 5.58/5.85  865 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom).  [assumption].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(865,b,806,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(865,b,807,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(865,b,808,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(865,b,809,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,810,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,811,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(865,b,812,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,813,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,814,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(865,b,815,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(865,b,816,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,817,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,818,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(865,b,819,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,820,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,821,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(865,b,822,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(865,b,823,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(865,b,824,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(865,b,825,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(865,b,826,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(865,b,827,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(865,b,828,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(865,b,829,b)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(865,b,830,b)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(865,b,831,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(865,b,832,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(865,b,833,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(865,b,834,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(865,b,835,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(865,b,836,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(865,b,837,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(865,b,838,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(865,b,839,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(865,b,840,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(865,b,841,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(865,b,842,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(865,b,843,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(865,b,844,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(865,b,845,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(865,b,846,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(865,b,847,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(865,b,848,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(865,b,849,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(865,b,850,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(865,b,851,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(865,b,852,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(865,b,853,a)].
% 5.58/5.85  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(865,b,854,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(865,b,855,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(865,b,856,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(865,b,857,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(865,b,858,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(865,b,859,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(865,b,860,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(865,b,861,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(865,b,862,a)].
% 5.66/5.86  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(865,b,863,a)].
% 5.66/5.86  866 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom).  [assumption].
% 5.66/5.86  Derived: class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(866,a,805,a)].
% 5.66/5.86  Derived: class_LOrder_Olorder(tc_nat).  [resolve(866,a,864,a)].
% 5.66/5.86  Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(866,a,865,b)].
% 5.66/5.86  867 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom).  [assumption].
% 5.66/5.86  Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint).  [resolve(867,a,805,a)].
% 5.66/5.86  Derived: class_LOrder_Ojoin__semilorder(tc_nat).  [resolve(867,a,864,a)].
% 5.66/5.86  Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(867,a,865,b)].
% 5.66/5.86  868 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom).  [assumption].
% 5.66/5.86  Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint).  [resolve(868,a,805,a)].
% 5.66/5.86  Derived: class_LOrder_Omeet__semilorder(tc_nat).  [resolve(868,a,864,a)].
% 5.66/5.86  Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(868,a,865,b)].
% 5.66/5.86  869 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom).  [assumption].
% 5.66/5.86  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(869,a,805,a)].
% 5.66/5.86  Derived: class_Orderings_Oord(tc_nat).  [resolve(869,a,864,a)].
% 5.66/5.86  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(869,a,865,b)].
% 5.66/5.86  870 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom).  [assumption].
% 5.66/5.86  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(870,a,805,a)].
% 5.66/5.86  Derived: class_Orderings_Oorder(tc_nat).  [resolve(870,a,864,a)].
% 5.66/5.86  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(870,a,865,b)].
% 5.66/5.87  871 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) # label(axiom).  [assumption].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(871,b,806,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(871,b,807,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(871,b,808,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(871,b,809,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,810,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,811,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(871,b,812,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,813,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,814,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(871,b,815,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(871,b,816,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,817,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,818,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(871,b,819,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,820,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,821,a)].
% 5.66/5.87  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(871,b,822,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(871,b,823,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(871,b,824,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(871,b,825,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(871,b,826,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(871,b,827,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(871,b,828,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(871,b,829,b)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(871,b,830,b)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(871,b,831,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(871,b,832,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(871,b,833,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(871,b,834,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(871,b,835,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(871,b,836,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(871,b,837,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(871,b,838,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(871,b,839,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(871,b,840,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(871,b,841,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(871,b,842,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(871,b,843,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(871,b,844,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(871,b,845,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(871,b,846,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(871,b,847,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(871,b,848,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(871,b,849,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(871,b,850,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(871,b,851,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(871,b,852,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(871,b,853,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(871,b,854,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(871,b,855,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(871,b,856,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(871,b,857,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(871,b,858,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(871,b,859,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(871,b,860,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(871,b,861,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(871,b,862,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(871,b,863,a)].
% 5.66/5.88  872 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom).  [assumption].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(872,b,806,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(872,b,807,a)].
% 5.66/5.88  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(872,b,808,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(872,b,809,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(872,b,810,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(872,b,811,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(872,b,812,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(872,b,813,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(872,b,814,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(872,b,815,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(872,b,816,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(872,b,817,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(872,b,818,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(872,b,819,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(872,b,820,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(872,b,821,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(872,b,822,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(872,b,823,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(872,b,824,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(872,b,825,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(872,b,826,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(872,b,827,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(872,b,828,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(872,b,829,b)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(872,b,830,b)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(872,b,831,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(872,b,832,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(872,b,833,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(872,b,834,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(872,b,835,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(872,b,836,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(872,b,837,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(872,b,838,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(872,b,839,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(872,b,840,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(872,b,841,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(872,b,842,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(872,b,843,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(872,b,844,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(872,b,845,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(872,b,846,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(872,b,847,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(872,b,848,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(872,b,849,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(872,b,850,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(872,b,851,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(872,b,852,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(872,b,853,a)].
% 5.69/5.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(872,b,854,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(872,b,855,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(872,b,856,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(872,b,857,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(872,b,858,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(872,b,859,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(872,b,860,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(872,b,861,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(872,b,862,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(872,b,863,a)].
% 5.69/5.90  873 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom).  [assumption].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(873,b,806,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(873,b,807,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(873,b,808,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(873,b,809,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(873,b,810,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(873,b,811,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(873,b,812,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(873,b,813,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(873,b,814,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(873,b,815,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(873,b,816,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(873,b,817,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(873,b,818,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(873,b,819,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(873,b,820,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(873,b,821,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(873,b,822,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(873,b,823,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(873,b,824,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(873,b,825,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(873,b,826,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(873,b,827,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(873,b,828,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(873,b,829,b)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(873,b,830,b)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(873,b,831,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(873,b,832,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(873,b,833,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(873,b,834,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(873,b,835,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(873,b,836,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(873,b,837,a)].
% 5.69/5.90  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(873,b,838,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(873,b,839,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(873,b,840,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(873,b,841,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(873,b,842,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(873,b,843,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(873,b,844,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(873,b,845,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(873,b,846,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(873,b,847,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(873,b,848,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(873,b,849,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(873,b,850,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(873,b,851,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(873,b,852,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(873,b,853,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(873,b,854,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(873,b,855,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(873,b,856,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(873,b,857,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(873,b,858,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(873,b,859,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(873,b,860,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(873,b,861,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(873,b,862,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(873,b,863,a)].
% 5.69/5.91  874 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom).  [assumption].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(874,b,806,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(874,b,807,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(874,b,808,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(874,b,809,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,810,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,811,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(874,b,812,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,813,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,814,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(874,b,815,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(874,b,816,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,817,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,818,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(874,b,819,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,820,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,821,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(874,b,822,a)].
% 5.69/5.91  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(874,b,823,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(874,b,824,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(874,b,825,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(874,b,826,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(874,b,827,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(874,b,828,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(874,b,829,b)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(874,b,830,b)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(874,b,831,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(874,b,832,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(874,b,833,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(874,b,834,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(874,b,835,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(874,b,836,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(874,b,837,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(874,b,838,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(874,b,839,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(874,b,840,a)].
% 5.69/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(874,b,841,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(874,b,842,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(874,b,843,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(874,b,844,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(874,b,845,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(874,b,846,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(874,b,847,a)].
% 5.72/5.92  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(874,b,848,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(874,b,849,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(874,b,850,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(874,b,851,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(874,b,852,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(874,b,853,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(874,b,854,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(874,b,855,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(874,b,856,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(874,b,857,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(874,b,858,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(874,b,859,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(874,b,860,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(874,b,861,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(874,b,862,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(874,b,863,a)].
% 5.72/5.93  875 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom).  [assumption].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(875,b,806,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(875,b,807,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(875,b,808,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(875,b,809,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,810,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,811,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(875,b,812,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,813,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,814,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(875,b,815,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(875,b,816,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,817,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,818,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(875,b,819,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,820,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,821,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(875,b,822,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(875,b,823,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(875,b,824,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(875,b,825,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(875,b,826,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(875,b,827,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(875,b,828,a)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(875,b,829,b)].
% 5.72/5.93  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(875,b,830,b)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(875,b,831,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(875,b,832,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(875,b,833,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(875,b,834,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(875,b,835,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(875,b,836,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(875,b,837,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(875,b,838,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(875,b,839,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(875,b,840,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(875,b,841,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(875,b,842,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(875,b,843,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(875,b,844,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(875,b,845,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(875,b,846,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(875,b,847,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(875,b,848,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(875,b,849,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(875,b,850,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(875,b,851,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(875,b,852,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(875,b,853,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(875,b,854,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(875,b,855,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(875,b,856,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(875,b,857,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(875,b,858,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(875,b,859,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(875,b,860,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(875,b,861,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(875,b,862,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(875,b,863,a)].
% 5.74/5.94  876 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom).  [assumption].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(876,b,806,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(876,b,807,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(876,b,808,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(876,b,809,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,810,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,811,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(876,b,812,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,813,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,814,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(876,b,815,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(876,b,816,a)].
% 5.74/5.94  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,817,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,818,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(876,b,819,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,820,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,821,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(876,b,822,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(876,b,823,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(876,b,824,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(876,b,825,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(876,b,826,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(876,b,827,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(876,b,828,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(876,b,829,b)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(876,b,830,b)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(876,b,831,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(876,b,832,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(876,b,833,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(876,b,834,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(876,b,835,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(876,b,836,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(876,b,837,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(876,b,838,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(876,b,839,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(876,b,840,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(876,b,841,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(876,b,842,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(876,b,843,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(876,b,844,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(876,b,845,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(876,b,846,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(876,b,847,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(876,b,848,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(876,b,849,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(876,b,850,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(876,b,851,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(876,b,852,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(876,b,853,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(876,b,854,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(876,b,855,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(876,b,856,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(876,b,857,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(876,b,858,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(876,b,859,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(876,b,860,a)].
% 5.74/5.95  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(876,b,861,a)].
% 5.74/5.96  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(876,b,862,a)].
% 5.74/5.96  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(876,b,863,a)].
% 5.74/5.96  877 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom).  [assumption].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(877,b,806,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(877,b,807,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(877,b,808,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(877,b,809,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,810,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,811,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(877,b,812,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,813,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,814,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,815,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(877,b,816,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,817,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,818,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(877,b,819,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,820,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,821,a)].
% 5.74/5.96  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(877,b,822,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(877,b,823,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(877,b,824,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,825,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(877,b,826,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(877,b,827,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(877,b,828,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(877,b,829,b)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(877,b,830,b)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(877,b,831,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(877,b,832,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(877,b,833,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(877,b,834,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(877,b,835,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(877,b,836,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(877,b,837,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(877,b,838,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(877,b,839,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(877,b,840,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(877,b,841,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(877,b,842,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(877,b,843,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(877,b,844,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(877,b,845,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(877,b,846,a)].
% 5.74/5.97  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(877,b,847,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(877,b,848,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(877,b,849,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(877,b,850,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(877,b,851,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(877,b,852,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(877,b,853,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(877,b,854,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(877,b,855,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(877,b,856,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(877,b,857,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(877,b,858,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(877,b,859,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(877,b,860,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(877,b,861,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(877,b,862,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(877,b,863,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A).  [resolve(877,b,866,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A).  [resolve(877,b,867,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A).  [resolve(877,b,868,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(877,b,869,a)].
% 6.02/6.22  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A).  [resolve(877,b,870,a)].
% 6.02/6.22  878 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom).  [assumption].
% 6.02/6.22  879 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_1 # label(cls_IntArith_Oabs__minus__one_0) # label(axiom).  [assumption].
% 6.02/6.22  880 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A),A) = c_1 # label(cls_IntArith_Oabs__power__minus__one_0) # label(axiom).  [assumption].
% 6.02/6.22  881 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__10_0) # label(axiom).  [assumption].
% 6.02/6.22  882 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__10_1) # label(axiom).  [assumption].
% 6.02/6.22  883 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__11_0) # label(axiom).  [assumption].
% 6.02/6.22  884 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_less(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__11_1) # label(axiom).  [assumption].
% 6.02/6.22  885 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__12_0) # label(axiom).  [assumption].
% 6.02/6.22  886 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__12_1) # label(axiom).  [assumption].
% 6.02/6.22  887 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_1,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__13_0) # label(axiom).  [assumption].
% 6.02/6.22  888 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__13_1) # label(axiom).  [assumption].
% 6.02/6.22  889 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_0) # label(axiom).  [assumption].
% 6.02/6.22  890 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_1) # label(axiom).  [assumption].
% 6.02/6.22  891 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | -c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_0) # label(axiom).  [assumption].
% 6.02/6.22  892 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_1) # label(axiom).  [assumption].
% 6.02/6.22  893 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_0) # label(axiom).  [assumption].
% 6.02/6.22  894 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_1) # label(axiom).  [assumption].
% 6.02/6.22  895 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_0) # label(axiom).  [assumption].
% 6.02/6.22  896 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_1) # label(axiom).  [assumption].
% 6.02/6.22  897 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_1,A) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A) # label(cls_IntArith_Oarith__special__1_0) # label(axiom).  [assumption].
% 6.02/6.22  898 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),B),A) # label(cls_IntArith_Oarith__special__2_0) # label(axiom).  [assumption].
% 6.02/6.22  899 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),A) # label(cls_IntArith_Oarith__special__3_0) # label(axiom).  [assumption].
% 6.02/6.22  900 -class_Numeral_Onumber__ring(A) | c_minus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A) # label(cls_IntArith_Oarith__special__4_0) # label(axiom).  [assumption].
% 6.02/6.22  901 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A) # label(cls_IntArith_Oarith__special__5_0) # label(axiom).  [assumption].
% 6.02/6.22  902 -class_Numeral_Onumber__ring(A) | c_0 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__6_0) # label(axiom).  [assumption].
% 6.02/6.22  903 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_0 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__6_1) # label(axiom).  [assumption].
% 6.02/6.22  904 -class_Numeral_Onumber__ring(A) | c_1 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__7_0) # label(axiom).  [assumption].
% 6.02/6.22  905 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_1 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__7_1) # label(axiom).  [assumption].
% 6.02/6.22  906 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__8_0) # label(axiom).  [assumption].
% 6.02/6.22  907 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_Numeral_Onumber__of(B,A) = c_0 # label(cls_IntArith_Oarith__special__8_1) # label(axiom).  [assumption].
% 6.02/6.22  908 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__9_0) # label(axiom).  [assumption].
% 6.02/6.22  909 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_Numeral_Onumber__of(B,A) = c_1 # label(cls_IntArith_Oarith__special__9_1) # label(axiom).  [assumption].
% 6.02/6.22  910 -class_Numeral_Onumber__ring(A) | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_IntArith_Oof__int__m1_0) # label(axiom).  [assumption].
% 6.02/6.22  911 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_0 # label(cls_NatBin_Oof__nat__number__of__eq_0) # label(axiom).  [assumption].
% 6.02/6.22  912 -class_Numeral_Onumber__ring(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_Numeral_Onumber__of(B,A) # label(cls_NatBin_Oof__nat__number__of__eq_1) # label(axiom).  [assumption].
% 6.02/6.22  913 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_NatSimprocs_Odivide__minus1_0) # label(axiom).  [assumption].
% 6.02/6.22  914 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | c_less(c_0,c_divide(B,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A),A),A) # label(cls_NatSimprocs_Ohalf__gt__zero_0) # label(axiom).  [assumption].
% 6.02/6.22  915 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(c_divide(c_1,B,A),A) # label(cls_NatSimprocs_Ominus1__divide_0) # label(axiom).  [assumption].
% 6.02/6.22  916 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_minus(C,c_Numeral_Onumber__of(D,A),A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(D)),A),C,A) # label(cls_Numeral_Oadd__number__of__diff2_0) # label(axiom).  [assumption].
% 6.02/6.22  917 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_plus(c_Numeral_Onumber__of(C,A),D,A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A),D,A) # label(cls_Numeral_Oadd__number__of__left_0) # label(axiom).  [assumption].
% 6.02/6.22  918 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__1_0) # label(axiom).  [assumption].
% 6.02/6.22  919 -class_Numeral_Onumber__ring(A) | c_uminus(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A) # label(cls_Numeral_Obin__arith__extra__simps__2_0) # label(axiom).  [assumption].
% 6.02/6.22  920 -class_Numeral_Onumber__ring(A) | c_uminus(c_1,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Numeral_Obin__arith__extra__simps__3_0) # label(axiom).  [assumption].
% 6.02/6.22  921 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__4_0) # label(axiom).  [assumption].
% 6.02/6.22  922 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A) # label(cls_Numeral_Obin__arith__extra__simps__5_0) # label(axiom).  [assumption].
% 6.02/6.22  923 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_uminus(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__arith__extra__simps__6_0) # label(axiom).  [assumption].
% 6.02/6.22  924 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(B,A) # label(cls_Numeral_Obin__arith__extra__simps__6_1) # label(axiom).  [assumption].
% 6.02/6.22  925 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__11_0) # label(axiom).  [assumption].
% 6.02/6.22  926 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__12_0) # label(axiom).  [assumption].
% 6.02/6.22  927 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) # label(cls_Numeral_Obin__rel__simps__12_1) # label(axiom).  [assumption].
% 6.02/6.22  928 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_0) # label(axiom).  [assumption].
% 6.02/6.22  929 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_1) # label(axiom).  [assumption].
% 6.02/6.22  930 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_Numeral_Onumber__of(C,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__1_0) # label(axiom).  [assumption].
% 6.02/6.22  931 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_Numeral_Onumber__of(B,A) = c_Numeral_Onumber__of(C,A) # label(cls_Numeral_Obin__rel__simps__1_1) # label(axiom).  [assumption].
% 6.02/6.22  932 -class_Numeral_Onumber__ring(A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__2_0) # label(axiom).  [assumption].
% 6.02/6.22  933 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__3_0) # label(axiom).  [assumption].
% 6.02/6.22  934 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__4_0) # label(axiom).  [assumption].
% 6.02/6.22  935 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) # label(cls_Numeral_Obin__rel__simps__4_1) # label(axiom).  [assumption].
% 6.02/6.22  936 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB1),A),A) # label(cls_Numeral_Obin__rel__simps__5_0) # label(axiom).  [assumption].
% 6.02/6.22  937 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__6_0) # label(axiom).  [assumption].
% 6.02/6.22  938 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) # label(cls_Numeral_Obin__rel__simps__6_1) # label(axiom).  [assumption].
% 6.02/6.22  939 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__7_0) # label(axiom).  [assumption].
% 6.02/6.23  940 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(c_Numeral_Onumber__of(B,A),A),C,A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A),C,A) # label(cls_Numeral_Ominus__number__of__mult_0) # label(axiom).  [assumption].
% 6.02/6.23  941 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1_0) # label(axiom).  [assumption].
% 6.02/6.23  942 -class_Numeral_Onumber__ring(A) | c_times(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1__right_0) # label(axiom).  [assumption].
% 6.02/6.23  943 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_times(c_Numeral_Onumber__of(C,A),D,A),A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A),D,A) # label(cls_Numeral_Omult__number__of__left_0) # label(axiom).  [assumption].
% 6.02/6.23  944 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OPls,A) = c_0 # label(cls_Numeral_Onumeral__0__eq__0_0) # label(axiom).  [assumption].
% 6.02/6.23  945 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A) = c_1 # label(cls_Numeral_Onumeral__1__eq__1_0) # label(axiom).  [assumption].
% 6.02/6.23  946 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_1 # label(cls_Parity_Oneg__one__even__power_0) # label(axiom).  [assumption].
% 6.02/6.23  947 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Parity_Oneg__one__odd__power_0) # label(axiom).  [assumption].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_1.  [resolve(878,a,879,a)].
% 6.02/6.23  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) = c_1.  [resolve(878,a,880,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,881,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,882,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,883,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,884,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,885,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(878,a,886,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,887,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint).  [resolve(878,a,888,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,889,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,890,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,891,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,892,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(878,a,893,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(878,a,894,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint).  [resolve(878,a,895,a)].
% 6.02/6.23  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint).  [resolve(878,a,896,a)].
% 6.02/6.23  Derived: c_plus(c_1,c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint).  [resolve(878,a,897,a)].
% 6.02/6.23  Derived: c_plus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A),tc_IntDef_Oint).  [resolve(878,a,898,a)].
% 6.02/6.23  Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint).  [resolve(878,a,899,a)].
% 6.02/6.23  Derived: c_minus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint).  [resolve(878,a,900,a)].
% 6.02/6.23  Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint).  [resolve(878,a,901,a)].
% 6.06/6.24  Derived: c_0 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,902,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_0 = c_Numeral_Onumber__of(A,tc_IntDef_Oint).  [resolve(878,a,903,a)].
% 6.06/6.24  Derived: c_1 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,904,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_1 = c_Numeral_Onumber__of(A,tc_IntDef_Oint).  [resolve(878,a,905,a)].
% 6.06/6.24  Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,906,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_0.  [resolve(878,a,907,a)].
% 6.06/6.24  Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,908,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_1.  [resolve(878,a,909,a)].
% 6.06/6.24  Derived: c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint).  [resolve(878,a,910,a)].
% 6.06/6.24  Derived: -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_0.  [resolve(878,a,911,a)].
% 6.06/6.24  Derived: c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint).  [resolve(878,a,912,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint).  [resolve(878,a,913,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_divide(A,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,914,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_divide(c_1,A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,915,a)].
% 6.06/6.24  Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(C)),tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(878,a,916,a)].
% 6.06/6.24  Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint).  [resolve(878,a,917,a)].
% 6.06/6.24  Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint).  [resolve(878,a,918,a)].
% 6.06/6.24  Derived: c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint).  [resolve(878,a,919,a)].
% 6.06/6.24  Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint).  [resolve(878,a,920,a)].
% 6.06/6.24  Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint).  [resolve(878,a,921,a)].
% 6.06/6.24  Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint).  [resolve(878,a,922,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,923,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint).  [resolve(878,a,924,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,925,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,926,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,927,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,928,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,929,a)].
% 6.06/6.24  Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_Numeral_Onumber__of(B,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,930,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_Numeral_Onumber__of(B,tc_IntDef_Oint).  [resolve(878,a,931,a)].
% 6.06/6.24  Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,932,a)].
% 6.06/6.24  Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,933,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,934,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,935,a)].
% 6.06/6.24  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB1),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,936,a)].
% 6.07/6.25  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,937,a)].
% 6.07/6.25  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,938,a)].
% 6.07/6.25  Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(878,a,939,a)].
% 6.07/6.25  Derived: c_times(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(878,a,940,a)].
% 6.07/6.25  Derived: c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint).  [resolve(878,a,941,a)].
% 6.07/6.25  Derived: c_times(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint).  [resolve(878,a,942,a)].
% 6.07/6.25  Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint).  [resolve(878,a,943,a)].
% 6.07/6.25  Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0.  [resolve(878,a,944,a)].
% 6.07/6.25  Derived: c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_IntDef_Oint) = c_1.  [resolve(878,a,945,a)].
% 6.07/6.25  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1.  [resolve(878,a,946,a)].
% 6.07/6.25  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint).  [resolve(878,a,947,a)].
% 6.07/6.25  948 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom).  [assumption].
% 6.07/6.25  949 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom).  [assumption].
% 6.07/6.25  950 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom).  [assumption].
% 6.07/6.25  951 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom).  [assumption].
% 6.07/6.25  952 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom).  [assumption].
% 6.07/6.25  953 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom).  [assumption].
% 6.07/6.25  954 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom).  [assumption].
% 6.07/6.25  Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint).  [resolve(954,a,878,a)].
% 6.07/6.25  955 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom).  [assumption].
% 6.07/6.25  956 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom).  [assumption].
% 6.07/6.25  Derived: class_Numeral_Onumber(tc_IntDef_Oint).  [resolve(956,a,878,a)].
% 6.07/6.25  957 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom).  [assumption].
% 6.07/6.25  958 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom).  [assumption].
% 6.07/6.25  959 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom).  [assumption].
% 6.13/6.31  960 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(6,b,1,a)].
% 6.13/6.31  961 -class_Numeral_Onumber__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(6,b,3,a)].
% 6.13/6.31  962 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(9,a,6,b)].
% 6.13/6.31  963 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(10,a,6,b)].
% 6.13/6.31  964 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(79,a,45,b)].
% 6.13/6.31  965 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(80,a,45,b)].
% 6.13/6.31  966 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(81,b,45,b)].
% 6.13/6.31  967 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(82,b,45,b)].
% 6.13/6.31  968 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(83,a,88,b)].
% 6.13/6.31  969 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(89,a,88,b)].
% 6.13/6.31  970 -class_Numeral_Onumber__ring(A) | c_times(c_1,B,A) = B.  [resolve(114,b,108,a)].
% 6.13/6.31  971 -class_Numeral_Onumber__ring(A) | c_times(B,c_1,A) = B.  [resolve(114,b,111,a)].
% 6.13/6.31  972 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(116,a,114,b)].
% 6.13/6.31  973 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(136,b,131,b)].
% 6.13/6.31  974 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(136,b,133,b)].
% 6.13/6.31  975 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(196,a,175,b)].
% 6.13/6.31  976 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(197,a,175,b)].
% 6.13/6.31  977 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(199,b,175,b)].
% 6.13/6.31  978 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(200,b,175,b)].
% 6.13/6.31  979 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(201,b,175,b)].
% 6.13/6.31  980 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(202,b,175,b)].
% 6.13/6.31  981 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(236,a,207,b)].
% 6.13/6.31  982 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(237,a,207,b)].
% 6.13/6.31  983 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(276,b,247,b)].
% 6.13/6.31  984 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(277,b,247,b)].
% 6.13/6.31  985 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(278,c,247,b)].
% 6.13/6.31  986 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(279,c,247,b)].
% 6.13/6.31  987 -class_Numeral_Onumber__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(285,b,280,a)].
% 6.13/6.31  988 -class_Numeral_Onumber__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(285,b,282,a)].
% 6.13/6.31  989 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(328,b,321,b)].
% 6.13/6.31  990 -class_Numeral_Onumber__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(328,b,323,b)].
% 6.13/6.33  991 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(328,b,324,a)].
% 6.13/6.33  992 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(328,b,325,a)].
% 6.13/6.33  993 -class_Numeral_Onumber__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(328,b,326,a)].
% 6.13/6.33  994 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(344,a,328,b)].
% 6.13/6.33  995 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(345,a,328,b)].
% 6.13/6.33  996 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(362,a,328,b)].
% 6.13/6.33  997 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(363,a,328,b)].
% 6.13/6.33  998 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(364,c,328,b)].
% 6.13/6.33  999 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(365,c,328,b)].
% 6.13/6.33  1000 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(397,b,371,b)].
% 6.13/6.33  1001 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(398,b,371,b)].
% 6.13/6.33  1002 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(439,b,410,b)].
% 6.13/6.33  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(1002,b,878,a)].
% 6.13/6.33  1003 class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A).  [resolve(440,b,410,b)].
% 6.13/6.33  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(1003,b,878,a)].
% 6.13/6.33  1004 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(443,b,410,b)].
% 6.13/6.33  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(1004,b,878,a)].
% 6.13/6.33  1005 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(444,b,410,b)].
% 6.13/6.33  1006 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(445,c,410,b)].
% 6.13/6.33  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1006,c,878,a)].
% 6.13/6.33  1007 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(446,c,410,b)].
% 6.13/6.33  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1007,c,878,a)].
% 6.13/6.33  1008 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A).  [resolve(451,a,410,b)].
% 6.13/6.33  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1008,c,878,a)].
% 6.13/6.33  1009 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Numeral_Onumber__ring(A).  [resolve(452,a,410,b)].
% 6.13/6.33  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1009,c,878,a)].
% 6.13/6.33  1010 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Numeral_Onumber__ring(B).  [resolve(453,a,410,b)].
% 6.13/6.35  Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint).  [resolve(1010,b,878,a)].
% 6.13/6.35  1011 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Numeral_Onumber__ring(B).  [resolve(454,a,410,b)].
% 6.13/6.35  Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1011,b,878,a)].
% 6.13/6.35  1012 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Numeral_Onumber__ring(C).  [resolve(455,a,410,b)].
% 6.13/6.35  Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1012,b,878,a)].
% 6.13/6.35  1013 class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(456,b,410,b)].
% 6.13/6.35  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(1013,b,878,a)].
% 6.13/6.35  1014 class_HOL_Ominus(A) | -class_Numeral_Onumber__ring(A).  [resolve(457,b,410,b)].
% 6.13/6.35  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(1014,b,878,a)].
% 6.13/6.35  1015 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(458,b,410,b)].
% 6.13/6.35  1016 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(459,b,410,b)].
% 6.13/6.35  1017 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C).  [resolve(460,c,410,b)].
% 6.13/6.35  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1017,c,878,a)].
% 6.13/6.35  1018 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C).  [resolve(461,c,410,b)].
% 6.13/6.35  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1018,c,878,a)].
% 6.13/6.35  1019 class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A).  [resolve(463,b,410,b)].
% 6.13/6.35  1020 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(464,b,410,b)].
% 6.13/6.35  1021 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(508,a,489,b)].
% 6.13/6.35  1022 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(509,a,489,b)].
% 6.13/6.35  1023 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Numeral_Onumber__ring(A).  [resolve(525,a,518,b)].
% 6.13/6.35  Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint).  [resolve(1023,b,878,a)].
% 6.13/6.35  1024 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(548,b,518,b)].
% 6.13/6.35  1025 c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(549,b,518,b)].
% 6.13/6.35  Derived: c_times(c_1,A,tc_IntDef_Oint) = A.  [resolve(1025,b,878,a)].
% 6.13/6.35  1026 c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B).  [resolve(550,b,518,b)].
% 6.13/6.35  Derived: c_times(A,c_1,tc_IntDef_Oint) = A.  [resolve(1026,b,878,a)].
% 6.13/6.35  1027 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(551,b,518,b)].
% 6.13/6.35  1028 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(552,b,518,b)].
% 6.13/6.35  1029 c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(639,b,593,b)].
% 6.13/6.35  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(1029,b,878,a)].
% 6.13/6.35  1030 c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B).  [resolve(640,b,593,b)].
% 6.13/6.35  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(1030,b,878,a)].
% 6.13/6.35  1031 class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A).  [resolve(642,b,593,b)].
% 6.13/6.35  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1031,b,878,a)].
% 6.13/6.35  1032 class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A).  [resolve(643,b,593,b)].
% 6.13/6.35  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(1032,b,878,a)].
% 6.13/6.35  1033 -class_Numeral_Onumber__ring(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(657,b,644,a)].
% 6.13/6.35  Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1033,a,878,a)].
% 6.13/6.35  1034 -class_Numeral_Onumber__ring(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(657,b,646,a)].
% 6.13/6.35  Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1034,a,878,a)].
% 6.13/6.35  1035 -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(657,b,647,a)].
% 6.13/6.35  Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1035,a,878,a)].
% 6.13/6.35  1036 -class_Numeral_Onumber__ring(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(657,b,648,a)].
% 6.36/6.54  Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1036,a,878,a)].
% 6.36/6.54  1037 -class_Numeral_Onumber__ring(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(657,b,649,a)].
% 6.36/6.54  Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint).  [resolve(1037,a,878,a)].
% 6.36/6.54  1038 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(657,b,650,a)].
% 6.36/6.54  Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint).  [resolve(1038,a,878,a)].
% 6.36/6.54  1039 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(657,b,651,a)].
% 6.36/6.54  Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1.  [resolve(1039,a,878,a)].
% 6.36/6.54  1040 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(657,b,652,a)].
% 6.36/6.54  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1040,a,878,a)].
% 6.36/6.54  1041 -class_Numeral_Onumber__ring(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(657,b,653,a)].
% 6.36/6.54  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1041,a,878,a)].
% 6.36/6.54  1042 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(657,b,654,a)].
% 6.36/6.54  Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint).  [resolve(1042,a,878,a)].
% 6.36/6.54  1043 class_HOL_Oone(A) | -class_Numeral_Onumber__ring(A).  [resolve(702,b,657,b)].
% 6.36/6.54  Derived: class_HOL_Oone(tc_IntDef_Oint).  [resolve(1043,b,878,a)].
% 6.36/6.54  1044 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(797,a,708,a)].
% 6.36/6.54  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1044,a,878,a)].
% 6.36/6.54  1045 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom).  [assumption].
% 6.36/6.54  1046 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom).  [assumption].
% 6.36/6.54  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1045,a,1046,a)].
% 6.36/6.54  1047 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom).  [assumption].
% 6.36/6.54  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(1047,a,1046,a)].
% 6.36/6.54  1048 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom).  [assumption].
% 6.36/6.54  1049 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom).  [assumption].
% 6.36/6.54  1050 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom).  [assumption].
% 6.36/6.54  Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1050,b,1046,a)].
% 6.36/6.54  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1050,b,1048,a)].
% 6.36/6.54  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A).  [resolve(1050,b,1049,a)].
% 6.36/6.54  1051 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom).  [assumption].
% 6.36/6.54  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1051,b,1046,a)].
% 6.36/6.54  1052 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom).  [assumption].
% 6.36/6.54  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1052,b,1046,a)].
% 6.36/6.54  1053 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1053,b,1046,a)].
% 6.62/6.81  1054 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1054,b,1046,a)].
% 6.62/6.81  1055 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1055,b,1046,a)].
% 6.62/6.81  1056 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1056,b,1046,a)].
% 6.62/6.81  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A).  [resolve(1056,b,1048,a)].
% 6.62/6.81  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1056,b,1049,a)].
% 6.62/6.81  1057 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1057,b,1046,a)].
% 6.62/6.81  1058 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1058,b,1046,a)].
% 6.62/6.81  1059 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1059,b,1046,a)].
% 6.62/6.81  1060 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_19) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1060,b,1046,a)].
% 6.62/6.81  1061 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1061,b,1046,a)].
% 6.62/6.81  1062 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_12) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1062,b,1046,a)].
% 6.62/6.81  1063 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom).  [assumption].
% 6.62/6.81  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1063,b,1046,a)].
% 6.62/6.81  1064 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint).  [resolve(867,a,805,a)].
% 6.62/6.81  1065 class_LOrder_Ojoin__semilorder(tc_nat).  [resolve(867,a,864,a)].
% 6.62/6.81  1066 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(867,a,865,b)].
% 6.62/6.81  1067 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A).  [resolve(877,b,867,a)].
% 6.62/6.81  1068 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom).  [assumption].
% 6.62/6.81  1069 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom).  [assumption].
% 6.62/6.81  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1068,a,1069,a)].
% 6.62/6.81  1070 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom).  [assumption].
% 6.62/6.83  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(1070,a,1069,a)].
% 6.62/6.83  1071 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1071,b,1069,a)].
% 6.62/6.83  1072 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom).  [assumption].
% 6.62/6.83  1073 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom).  [assumption].
% 6.62/6.83  1074 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1074,b,1069,a)].
% 6.62/6.83  1075 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1075,b,1069,a)].
% 6.62/6.83  1076 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1076,b,1069,a)].
% 6.62/6.83  1077 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1077,b,1069,a)].
% 6.62/6.83  1078 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1078,b,1069,a)].
% 6.62/6.83  1079 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1079,b,1069,a)].
% 6.62/6.83  1080 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1080,b,1069,a)].
% 6.62/6.83  1081 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1081,b,1069,a)].
% 6.62/6.83  1082 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1082,b,1069,a)].
% 6.62/6.83  1083 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_20) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1083,b,1069,a)].
% 6.62/6.83  1084 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1084,b,1069,a)].
% 6.62/6.83  1085 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_13) # label(axiom).  [assumption].
% 6.62/6.83  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1085,b,1069,a)].
% 6.87/7.08  1086 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom).  [assumption].
% 6.87/7.08  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1086,b,1069,a)].
% 6.87/7.08  1087 class_LOrder_Omeet__semilorder(tc_IntDef_Oint).  [resolve(868,a,805,a)].
% 6.87/7.08  1088 class_LOrder_Omeet__semilorder(tc_nat).  [resolve(868,a,864,a)].
% 6.87/7.08  1089 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(868,a,865,b)].
% 6.87/7.08  1090 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A).  [resolve(877,b,868,a)].
% 6.87/7.08  1091 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom).  [assumption].
% 6.87/7.08  1092 -class_Ring__and__Field_Oordered__semidom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B # label(cls_NatArith_Oof__nat__0__eq__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1093 -class_Ring__and__Field_Oordered__semidom(A) | c_0 = c_NatArith_Oof__nat(c_0,A) # label(cls_NatArith_Oof__nat__0__eq__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1094 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__le__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1095 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat) # label(cls_NatArith_Oof__nat__0__less__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1096 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__less__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1097 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1098 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_0,A) = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1099 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C # label(cls_NatArith_Oof__nat__eq__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1100 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0 # label(cls_NatArith_Oof__nat__le__0__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1101 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) # label(cls_NatArith_Oof__nat__le__0__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1102 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat) # label(cls_NatArith_Oof__nat__le__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1103 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__le__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1104 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A) # label(cls_NatArith_Oof__nat__less__0__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1105 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat) # label(cls_NatArith_Oof__nat__less__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1106 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__less__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1107 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat) # label(cls_Power_Opower__increasing__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1108 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) # label(cls_Power_Opower__increasing__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1109 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D # label(cls_Power_Opower__inject__exp_0) # label(axiom).  [assumption].
% 6.87/7.08  1110 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat) # label(cls_Power_Opower__strict__increasing__iff_0) # label(axiom).  [assumption].
% 6.87/7.08  1111 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A) # label(cls_Power_Opower__strict__increasing__iff_1) # label(axiom).  [assumption].
% 6.87/7.08  1112 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__le__zero_0) # label(axiom).  [assumption].
% 6.87/7.08  1113 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__less__zero_0) # label(axiom).  [assumption].
% 6.87/7.08  1114 -class_Ring__and__Field_Oordered__semidom(A) | c_less(c_0,c_1,A) # label(cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) # label(axiom).  [assumption].
% 6.87/7.08  1115 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_1,A) # label(cls_Ring__and__Field_Ozero__le__one_0) # label(axiom).  [assumption].
% 6.87/7.08  Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A.  [resolve(1091,a,1092,a)].
% 6.87/7.08  Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint).  [resolve(1091,a,1093,a)].
% 6.87/7.08  Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1094,a)].
% 6.87/7.08  Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat).  [resolve(1091,a,1095,a)].
% 6.87/7.08  Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1096,a)].
% 6.87/7.08  Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1091,a,1097,a)].
% 6.87/7.08  Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0.  [resolve(1091,a,1098,a)].
% 6.87/7.08  Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B.  [resolve(1091,a,1099,a)].
% 6.87/7.08  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(1091,a,1100,a)].
% 6.87/7.08  Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1091,a,1101,a)].
% 6.87/7.08  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_nat).  [resolve(1091,a,1102,a)].
% 6.87/7.08  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1103,a)].
% 6.87/7.08  Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1091,a,1104,a)].
% 6.87/7.08  Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_nat).  [resolve(1091,a,1105,a)].
% 6.87/7.08  Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1106,a)].
% 6.87/7.08  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_nat).  [resolve(1091,a,1107,b)].
% 6.87/7.08  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1108,b)].
% 6.87/7.08  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | c_Nat_Opower(A,B,tc_IntDef_Oint) != c_Nat_Opower(A,C,tc_IntDef_Oint) | B = C.  [resolve(1091,a,1109,b)].
% 6.87/7.08  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_less(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_nat).  [resolve(1091,a,1110,b)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_IntDef_Oint) | c_less(c_Nat_Opower(C,A,tc_IntDef_Oint),c_Nat_Opower(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1091,a,1111,b)].
% 6.92/7.10  Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint).  [resolve(1091,a,1112,a)].
% 6.92/7.10  Derived: -c_less(c_1,c_0,tc_IntDef_Oint).  [resolve(1091,a,1113,a)].
% 6.92/7.10  Derived: c_less(c_0,c_1,tc_IntDef_Oint).  [resolve(1091,a,1114,a)].
% 6.92/7.10  Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint).  [resolve(1091,a,1115,a)].
% 6.92/7.10  1116 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom).  [assumption].
% 6.92/7.10  Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A.  [resolve(1116,a,1092,a)].
% 6.92/7.10  Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat).  [resolve(1116,a,1093,a)].
% 6.92/7.10  Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat).  [resolve(1116,a,1094,a)].
% 6.92/7.10  Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat).  [resolve(1116,a,1095,a)].
% 6.92/7.10  Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat).  [resolve(1116,a,1096,a)].
% 6.92/7.10  Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0.  [resolve(1116,a,1097,a)].
% 6.92/7.10  Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0.  [resolve(1116,a,1098,a)].
% 6.92/7.10  Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B.  [resolve(1116,a,1099,a)].
% 6.92/7.10  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0.  [resolve(1116,a,1100,a)].
% 6.92/7.10  Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat).  [resolve(1116,a,1101,a)].
% 6.92/7.10  Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1116,a,1102,a)].
% 6.92/7.10  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(1116,a,1103,a)].
% 6.92/7.10  Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat).  [resolve(1116,a,1104,a)].
% 6.92/7.10  Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1116,a,1105,a)].
% 6.92/7.10  Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(1116,a,1106,a)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(1116,a,1107,b)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat).  [resolve(1116,a,1108,b)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | c_Nat_Opower(A,B,tc_nat) != c_Nat_Opower(A,C,tc_nat) | B = C.  [resolve(1116,a,1109,b)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_less(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat).  [resolve(1116,a,1110,b)].
% 6.92/7.10  Derived: -class_Power_Orecpower(tc_nat) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_nat) | c_less(c_Nat_Opower(C,A,tc_nat),c_Nat_Opower(C,B,tc_nat),tc_nat).  [resolve(1116,a,1111,b)].
% 6.92/7.10  Derived: -c_lessequals(c_1,c_0,tc_nat).  [resolve(1116,a,1112,a)].
% 6.92/7.10  Derived: -c_less(c_1,c_0,tc_nat).  [resolve(1116,a,1113,a)].
% 6.92/7.10  Derived: c_less(c_0,c_1,tc_nat).  [resolve(1116,a,1114,a)].
% 6.92/7.10  Derived: c_lessequals(c_0,c_1,tc_nat).  [resolve(1116,a,1115,a)].
% 6.92/7.10  1117 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semidom(A) # label(clsrel_Ring__and__Field_Oordered__field_60) # label(axiom).  [assumption].
% 6.92/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B.  [resolve(1117,b,1092,a)].
% 6.92/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A).  [resolve(1117,b,1093,a)].
% 6.92/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1117,b,1094,a)].
% 6.92/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat).  [resolve(1117,b,1095,a)].
% 6.92/7.10  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1117,b,1096,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0.  [resolve(1117,b,1097,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0.  [resolve(1117,b,1098,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C.  [resolve(1117,b,1099,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0.  [resolve(1117,b,1100,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A).  [resolve(1117,b,1101,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat).  [resolve(1117,b,1102,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(1117,b,1103,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A).  [resolve(1117,b,1104,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat).  [resolve(1117,b,1105,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(1117,b,1106,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat).  [resolve(1117,b,1107,b)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A).  [resolve(1117,b,1108,b)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D.  [resolve(1117,b,1109,b)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat).  [resolve(1117,b,1110,b)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A).  [resolve(1117,b,1111,b)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A).  [resolve(1117,b,1112,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A).  [resolve(1117,b,1113,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A).  [resolve(1117,b,1114,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A).  [resolve(1117,b,1115,a)].
% 6.92/7.11  1118 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__semidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_55) # label(axiom).  [assumption].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B.  [resolve(1118,b,1092,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A).  [resolve(1118,b,1093,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1118,b,1094,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat).  [resolve(1118,b,1095,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A).  [resolve(1118,b,1096,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0.  [resolve(1118,b,1097,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0.  [resolve(1118,b,1098,a)].
% 6.92/7.11  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C.  [resolve(1118,b,1099,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0.  [resolve(1118,b,1100,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A).  [resolve(1118,b,1101,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat).  [resolve(1118,b,1102,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(1118,b,1103,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A).  [resolve(1118,b,1104,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat).  [resolve(1118,b,1105,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(1118,b,1106,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat).  [resolve(1118,b,1107,b)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A).  [resolve(1118,b,1108,b)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D.  [resolve(1118,b,1109,b)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat).  [resolve(1118,b,1110,b)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A).  [resolve(1118,b,1111,b)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A).  [resolve(1118,b,1112,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A).  [resolve(1118,b,1113,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A).  [resolve(1118,b,1114,a)].
% 6.92/7.12  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A).  [resolve(1118,b,1115,a)].
% 6.92/7.12  1119 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom).  [assumption].
% 6.92/7.12  1120 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom).  [assumption].
% 6.92/7.12  1121 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom).  [assumption].
% 6.92/7.12  1122 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom).  [assumption].
% 6.92/7.12  1123 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom).  [assumption].
% 6.92/7.12  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1123,a,1118,b)].
% 6.92/7.12  1124 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom).  [assumption].
% 6.92/7.12  1125 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom).  [assumption].
% 6.92/7.12  1126 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__semidom_24) # label(axiom).  [assumption].
% 6.92/7.12  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint).  [resolve(1126,a,1091,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).  [resolve(1126,a,1116,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1126,a,1117,b)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1126,a,1118,b)].
% 6.92/7.13  1127 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__semidom_25) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint).  [resolve(1127,a,1091,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat).  [resolve(1127,a,1116,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1127,a,1117,b)].
% 6.92/7.13  Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1127,a,1118,b)].
% 6.92/7.13  1128 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_26) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1128,a,1091,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1128,a,1116,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1128,a,1117,b)].
% 6.92/7.13  Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1128,a,1118,b)].
% 6.92/7.13  1129 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1129,a,1117,b)].
% 6.92/7.13  Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1129,a,1118,b)].
% 6.92/7.13  1130 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__semidom_31) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1130,a,1091,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).  [resolve(1130,a,1116,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1130,a,1117,b)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1130,a,1118,b)].
% 6.92/7.13  1131 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_32) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1131,a,1091,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1131,a,1116,a)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1131,a,1117,b)].
% 6.92/7.13  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1131,a,1118,b)].
% 6.92/7.13  1132 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_33) # label(axiom).  [assumption].
% 6.92/7.13  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint).  [resolve(1132,a,1091,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat).  [resolve(1132,a,1116,a)].
% 6.92/7.13  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1132,a,1117,b)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1132,a,1118,b)].
% 6.97/7.15  1133 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_34) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint).  [resolve(1133,a,1091,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).  [resolve(1133,a,1116,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1133,a,1117,b)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1133,a,1118,b)].
% 6.97/7.15  1134 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_35) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint).  [resolve(1134,a,1091,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat).  [resolve(1134,a,1116,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1134,a,1117,b)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1134,a,1118,b)].
% 6.97/7.15  1135 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_36) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint).  [resolve(1135,a,1091,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__semiring(tc_nat).  [resolve(1135,a,1116,a)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1135,a,1117,b)].
% 6.97/7.15  Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1135,a,1118,b)].
% 6.97/7.15  1136 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_37) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1136,a,1091,a)].
% 6.97/7.15  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).  [resolve(1136,a,1116,a)].
% 6.97/7.15  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1136,a,1117,b)].
% 6.97/7.15  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1136,a,1118,b)].
% 6.97/7.15  1137 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1137,a,1117,b)].
% 6.97/7.15  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1137,a,1118,b)].
% 6.97/7.15  1138 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom).  [assumption].
% 6.97/7.15  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1138,a,1117,b)].
% 6.97/7.15  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1138,a,1118,b)].
% 6.97/7.15  1139 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom).  [assumption].
% 6.97/7.15  1140 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(31,b,1,a)].
% 6.97/7.15  1141 -class_Ring__and__Field_Oordered__semidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(31,b,3,a)].
% 6.97/7.15  1142 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(81,b,69,b)].
% 6.97/7.15  1143 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(82,b,69,b)].
% 6.97/7.15  1144 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_1,B,A) = B.  [resolve(127,b,108,a)].
% 6.97/7.20  1145 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_1,A) = B.  [resolve(127,b,111,a)].
% 6.97/7.20  1146 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A).  [resolve(127,b,117,a)].
% 6.97/7.20  1147 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A).  [resolve(127,b,118,a)].
% 6.97/7.20  1148 -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(152,b,131,b)].
% 6.97/7.20  1149 -class_Ring__and__Field_Oordered__semidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(152,b,133,b)].
% 6.97/7.20  1150 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(199,b,192,b)].
% 6.97/7.20  1151 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(200,b,192,b)].
% 6.97/7.21  1152 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(201,b,192,b)].
% 6.97/7.21  1153 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(202,b,192,b)].
% 6.97/7.21  1154 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(236,a,222,b)].
% 6.97/7.21  1155 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(237,a,222,b)].
% 6.97/7.21  1156 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(241,a,222,b)].
% 6.97/7.21  1157 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(242,a,222,b)].
% 6.97/7.21  1158 -class_Ring__and__Field_Oordered__semidom(A) | c_times(c_0,B,A) = c_0.  [resolve(298,b,280,a)].
% 6.97/7.21  1159 -class_Ring__and__Field_Oordered__semidom(A) | c_times(B,c_0,A) = c_0.  [resolve(298,b,282,a)].
% 6.97/7.21  1160 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semidom(C).  [resolve(314,a,298,b)].
% 6.97/7.21  1161 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semidom(C).  [resolve(315,a,298,b)].
% 6.97/7.21  1162 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(501,a,498,b)].
% 6.97/7.21  1163 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(508,a,498,b)].
% 6.97/7.21  1164 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(509,a,498,b)].
% 6.97/7.21  1165 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(513,a,498,b)].
% 6.97/7.21  1166 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(551,b,534,b)].
% 6.97/7.21  1167 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(585,a,565,b)].
% 6.97/7.21  1168 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B).  [resolve(586,a,565,b)].
% 6.97/7.21  1169 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(589,b,565,b)].
% 6.97/7.21  1170 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(673,b,644,a)].
% 6.97/7.21  Derived: c_in(c_0,c_IntDef_ONats,tc_nat).  [resolve(1170,a,1116,a)].
% 6.97/7.21  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1170,a,1117,b)].
% 6.97/7.21  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1170,a,1118,b)].
% 6.97/7.21  1171 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(673,b,646,a)].
% 6.97/7.21  Derived: c_in(c_1,c_IntDef_ONats,tc_nat).  [resolve(1171,a,1116,a)].
% 6.97/7.21  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1171,a,1117,b)].
% 6.97/7.21  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1171,a,1118,b)].
% 6.97/7.21  1172 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(673,b,647,a)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(1172,a,1116,a)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1172,a,1117,b)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1172,a,1118,b)].
% 6.97/7.21  1173 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(673,b,648,a)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(1173,a,1116,a)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1173,a,1117,b)].
% 6.97/7.21  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1173,a,1118,b)].
% 6.97/7.21  1174 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(673,b,649,a)].
% 6.97/7.21  Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat).  [resolve(1174,a,1116,a)].
% 6.97/7.21  Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1174,a,1117,b)].
% 6.97/7.21  Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1174,a,1118,b)].
% 6.97/7.21  1175 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(673,b,650,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat).  [resolve(1175,a,1116,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1175,a,1117,b)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1175,a,1118,b)].
% 6.97/7.21  1176 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(673,b,651,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1.  [resolve(1176,a,1116,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A).  [resolve(1176,a,1117,b)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1176,a,1118,b)].
% 6.97/7.21  1177 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(673,b,652,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(1177,a,1116,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1177,a,1117,b)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1177,a,1118,b)].
% 6.97/7.21  1178 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(673,b,653,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat).  [resolve(1178,a,1116,a)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1178,a,1117,b)].
% 6.97/7.21  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1178,a,1118,b)].
% 7.07/7.26  1179 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(673,b,654,a)].
% 7.07/7.26  Derived: -c_IntDef_Oiszero(c_1,tc_nat).  [resolve(1179,a,1116,a)].
% 7.07/7.26  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1179,a,1117,b)].
% 7.07/7.26  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1179,a,1118,b)].
% 7.07/7.26  1180 class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__semidom(A).  [resolve(702,b,673,b)].
% 7.07/7.26  Derived: class_HOL_Oone(tc_nat).  [resolve(1180,b,1116,a)].
% 7.07/7.26  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1180,b,1117,b)].
% 7.07/7.26  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1180,b,1118,b)].
% 7.07/7.26  1181 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(794,a,708,a)].
% 7.07/7.26  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(1181,a,1116,a)].
% 7.07/7.26  1182 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A).  [resolve(794,a,715,a)].
% 7.07/7.26  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1182,a,1117,b)].
% 7.07/7.26  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1182,a,1118,b)].
% 7.07/7.26  1183 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(875,b,806,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset.  [resolve(1183,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset.  [resolve(1183,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1183,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1183,a,1118,b)].
% 7.07/7.26  1184 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(875,b,807,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1184,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(1184,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1184,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1184,a,1118,b)].
% 7.07/7.26  1185 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(875,b,808,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1185,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat).  [resolve(1185,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1185,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1185,a,1118,b)].
% 7.07/7.26  1186 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(875,b,809,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(1186,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset.  [resolve(1186,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1186,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1186,a,1118,b)].
% 7.07/7.26  1187 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,810,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1187,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(1187,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1187,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1187,a,1118,b)].
% 7.07/7.26  1188 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,811,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1188,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(1188,a,1116,a)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1188,a,1117,b)].
% 7.07/7.26  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1188,a,1118,b)].
% 7.07/7.26  1189 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(875,b,812,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(1189,a,1091,a)].
% 7.07/7.26  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset.  [resolve(1189,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1189,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1189,a,1118,b)].
% 7.07/7.27  1190 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,813,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1190,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(1190,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1190,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1190,a,1118,b)].
% 7.07/7.27  1191 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(875,b,814,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1191,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(1191,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1191,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1191,a,1118,b)].
% 7.07/7.27  1192 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(875,b,815,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1192,a,1091,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(1192,a,1116,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1192,a,1117,b)].
% 7.07/7.27  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1192,a,1118,b)].
% 7.07/7.27  1193 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(875,b,816,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(1193,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset.  [resolve(1193,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1193,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1193,a,1118,b)].
% 7.07/7.27  1194 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,817,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(1194,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(1194,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1194,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1194,a,1118,b)].
% 7.07/7.27  1195 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,818,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(1195,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(1195,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1195,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1195,a,1118,b)].
% 7.07/7.27  1196 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(875,b,819,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(1196,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset.  [resolve(1196,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1196,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1196,a,1118,b)].
% 7.07/7.27  1197 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,820,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(1197,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(1197,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1197,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1197,a,1118,b)].
% 7.07/7.27  1198 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(875,b,821,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(1198,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(1198,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1198,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1198,a,1118,b)].
% 7.07/7.27  1199 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(875,b,822,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(1199,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(1199,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1199,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1199,a,1118,b)].
% 7.07/7.27  1200 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(875,b,823,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1200,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat).  [resolve(1200,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1200,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1200,a,1118,b)].
% 7.07/7.27  1201 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(875,b,824,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(1201,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset.  [resolve(1201,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1201,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1201,a,1118,b)].
% 7.07/7.27  1202 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(875,b,825,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1202,a,1091,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(1202,a,1116,a)].
% 7.07/7.27  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1202,a,1117,b)].
% 7.07/7.27  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1202,a,1118,b)].
% 7.07/7.27  1203 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(875,b,826,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(1203,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(1203,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(1203,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1203,a,1118,b)].
% 7.07/7.27  1204 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(875,b,827,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1204,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A.  [resolve(1204,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C).  [resolve(1204,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1204,a,1118,b)].
% 7.07/7.27  1205 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(875,b,828,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(1205,a,1091,a)].
% 7.07/7.27  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A.  [resolve(1205,a,1116,a)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C).  [resolve(1205,a,1117,b)].
% 7.07/7.27  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1205,a,1118,b)].
% 7.07/7.27  1206 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(875,b,829,b)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint).  [resolve(1206,a,1091,a)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat).  [resolve(1206,a,1116,a)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1206,a,1117,b)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1206,a,1118,b)].
% 7.07/7.27  1207 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(875,b,830,b)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1207,a,1091,a)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat).  [resolve(1207,a,1116,a)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1207,a,1117,b)].
% 7.07/7.27  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1207,a,1118,b)].
% 7.07/7.27  1208 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(875,b,831,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1208,a,1091,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(1208,a,1116,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1208,a,1117,b)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1208,a,1118,b)].
% 7.07/7.27  1209 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(875,b,832,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(1209,a,1091,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(1209,a,1116,a)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1209,a,1117,b)].
% 7.07/7.27  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1209,a,1118,b)].
% 7.07/7.27  1210 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(875,b,833,a)].
% 7.07/7.27  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(1210,a,1091,a)].
% 7.07/7.27  Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(1210,a,1116,a)].
% 7.07/7.27  Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1210,a,1117,b)].
% 7.07/7.27  Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1210,a,1118,b)].
% 7.07/7.28  1211 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(875,b,834,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(1211,a,1091,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1211,a,1116,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1211,a,1117,b)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1211,a,1118,b)].
% 7.07/7.28  1212 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(875,b,835,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1212,a,1091,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1212,a,1116,a)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1212,a,1117,b)].
% 7.07/7.28  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1212,a,1118,b)].
% 7.07/7.28  1213 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(875,b,836,a)].
% 7.07/7.28  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1213,a,1091,a)].
% 7.07/7.28  Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(1213,a,1116,a)].
% 7.07/7.28  Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1213,a,1117,b)].
% 7.07/7.28  Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1213,a,1118,b)].
% 7.07/7.28  1214 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(875,b,837,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1214,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1214,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1214,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1214,a,1118,b)].
% 7.07/7.28  1215 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(875,b,838,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1215,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1215,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1215,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1215,a,1118,b)].
% 7.07/7.28  1216 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(875,b,839,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1216,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(1216,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1216,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1216,a,1118,b)].
% 7.07/7.28  1217 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(875,b,840,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(1217,a,1091,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(1217,a,1116,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1217,a,1117,b)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1217,a,1118,b)].
% 7.07/7.28  1218 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(875,b,841,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint).  [resolve(1218,a,1091,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat).  [resolve(1218,a,1116,a)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1218,a,1117,b)].
% 7.07/7.28  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1218,a,1118,b)].
% 7.07/7.28  1219 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(875,b,842,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1219,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1219,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1219,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1219,a,1118,b)].
% 7.07/7.28  1220 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(875,b,843,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(1220,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(1220,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1220,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1220,a,1118,b)].
% 7.07/7.28  1221 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(875,b,844,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(1221,a,1091,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(1221,a,1116,a)].
% 7.07/7.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1221,a,1117,b)].
% 7.07/7.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1221,a,1118,b)].
% 7.07/7.28  1222 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(875,b,845,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(1222,a,1091,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(1222,a,1116,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1222,a,1117,b)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1222,a,1118,b)].
% 7.07/7.28  1223 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(875,b,846,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint).  [resolve(1223,a,1091,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat).  [resolve(1223,a,1116,a)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1223,a,1117,b)].
% 7.07/7.28  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1223,a,1118,b)].
% 7.07/7.28  1224 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(875,b,847,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint).  [resolve(1224,a,1091,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(1224,a,1116,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1224,a,1117,b)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1224,a,1118,b)].
% 7.07/7.28  1225 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(875,b,848,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint).  [resolve(1225,a,1091,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(1225,a,1116,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1225,a,1117,b)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1225,a,1118,b)].
% 7.07/7.28  1226 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(875,b,849,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint).  [resolve(1226,a,1091,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(1226,a,1116,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1226,a,1117,b)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1226,a,1118,b)].
% 7.07/7.28  1227 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(875,b,850,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint).  [resolve(1227,a,1091,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(1227,a,1116,a)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1227,a,1117,b)].
% 7.07/7.28  Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1227,a,1118,b)].
% 7.07/7.28  1228 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(875,b,851,a)].
% 7.07/7.28  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(1228,a,1091,a)].
% 7.07/7.28  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(1228,a,1116,a)].
% 7.07/7.29  Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(1228,a,1117,b)].
% 7.07/7.29  Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1228,a,1118,b)].
% 7.07/7.29  1229 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(875,b,852,a)].
% 7.07/7.29  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(1229,a,1091,a)].
% 7.07/7.29  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(1229,a,1116,a)].
% 7.07/7.29  Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(1229,a,1117,b)].
% 7.07/7.29  Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1229,a,1118,b)].
% 7.07/7.29  1230 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(875,b,853,a)].
% 7.07/7.29  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(1230,a,1091,a)].
% 7.07/7.29  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(1230,a,1116,a)].
% 7.07/7.29  Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(1230,a,1117,b)].
% 7.07/7.29  Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1230,a,1118,b)].
% 7.07/7.29  1231 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(875,b,854,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1231,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(1231,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1231,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1231,a,1118,b)].
% 7.07/7.29  1232 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(875,b,855,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1232,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)).  [resolve(1232,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1232,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1232,a,1118,b)].
% 7.07/7.29  1233 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(875,b,856,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint).  [resolve(1233,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat).  [resolve(1233,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1233,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1233,a,1118,b)].
% 7.07/7.29  1234 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(875,b,857,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1234,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1234,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1234,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1234,a,1118,b)].
% 7.07/7.29  1235 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(875,b,858,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1235,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1235,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1235,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1235,a,1118,b)].
% 7.07/7.29  1236 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(875,b,859,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1236,a,1091,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)).  [resolve(1236,a,1116,a)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1236,a,1117,b)].
% 7.07/7.29  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1236,a,1118,b)].
% 7.07/7.29  1237 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(875,b,860,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1237,a,1091,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)).  [resolve(1237,a,1116,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1237,a,1117,b)].
% 7.11/7.32  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1237,a,1118,b)].
% 7.11/7.32  1238 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(875,b,861,a)].
% 7.11/7.32  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(1238,a,1091,a)].
% 7.11/7.32  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(1238,a,1116,a)].
% 7.11/7.32  Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(1238,a,1117,b)].
% 7.11/7.32  Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1238,a,1118,b)].
% 7.11/7.32  1239 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(875,b,862,a)].
% 7.11/7.32  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1239,a,1091,a)].
% 7.11/7.32  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(1239,a,1116,a)].
% 7.11/7.32  Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1239,a,1117,b)].
% 7.11/7.32  Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1239,a,1118,b)].
% 7.11/7.32  1240 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(875,b,863,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1240,a,1091,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)).  [resolve(1240,a,1116,a)].
% 7.11/7.32  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1240,a,1117,b)].
% 7.11/7.32  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1240,a,1118,b)].
% 7.11/7.32  1241 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1061,b,1046,a)].
% 7.11/7.32  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1241,a,1091,a)].
% 7.11/7.32  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(1241,a,1116,a)].
% 7.11/7.32  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1241,a,1117,b)].
% 7.11/7.32  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1241,a,1118,b)].
% 7.11/7.32  1242 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1084,b,1069,a)].
% 7.27/7.47  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1242,a,1091,a)].
% 7.27/7.47  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(1242,a,1116,a)].
% 7.27/7.47  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(1242,a,1117,b)].
% 7.27/7.47  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1242,a,1118,b)].
% 7.27/7.47  1243 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom).  [assumption].
% 7.27/7.47  1244 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_0) # label(axiom).  [assumption].
% 7.27/7.47  1245 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_1) # label(axiom).  [assumption].
% 7.27/7.47  1246 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_2) # label(axiom).  [assumption].
% 7.27/7.47  1247 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_3) # label(axiom).  [assumption].
% 7.27/7.47  1248 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_4) # label(axiom).  [assumption].
% 7.27/7.47  1249 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_5) # label(axiom).  [assumption].
% 7.27/7.47  1250 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_0) # label(axiom).  [assumption].
% 7.27/7.47  1251 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_1) # label(axiom).  [assumption].
% 7.27/7.47  1252 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_2) # label(axiom).  [assumption].
% 7.27/7.47  1253 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_3) # label(axiom).  [assumption].
% 7.27/7.47  1254 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_4) # label(axiom).  [assumption].
% 7.27/7.47  1255 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_5) # label(axiom).  [assumption].
% 7.27/7.47  1256 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_0) # label(axiom).  [assumption].
% 7.27/7.47  1257 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_1) # label(axiom).  [assumption].
% 7.27/7.47  1258 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_2) # label(axiom).  [assumption].
% 7.27/7.47  1259 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_3) # label(axiom).  [assumption].
% 7.27/7.47  1260 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_4) # label(axiom).  [assumption].
% 7.27/7.47  1261 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_5) # label(axiom).  [assumption].
% 7.27/7.47  1262 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_0) # label(axiom).  [assumption].
% 7.27/7.47  1263 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_1) # label(axiom).  [assumption].
% 7.27/7.47  1264 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_2) # label(axiom).  [assumption].
% 7.27/7.47  1265 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_3) # label(axiom).  [assumption].
% 7.27/7.47  1266 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_4) # label(axiom).  [assumption].
% 7.27/7.47  1267 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_5) # label(axiom).  [assumption].
% 7.27/7.47  1268 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0 # label(cls_Ring__and__Field_Omult__eq__0__iff_0) # label(axiom).  [assumption].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(1243,a,1244,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint).  [resolve(1243,a,1245,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1246,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1247,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1248,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1249,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(1243,a,1250,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint).  [resolve(1243,a,1251,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1252,b)].
% 7.27/7.47  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1253,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1254,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1255,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(1243,a,1256,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,B,tc_IntDef_Oint).  [resolve(1243,a,1257,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1243,a,1258,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1259,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1243,a,1260,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1261,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1243,a,1262,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint).  [resolve(1243,a,1263,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1243,a,1264,b)].
% 7.27/7.48  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1265,b)].
% 7.27/7.49  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1243,a,1266,b)].
% 7.27/7.49  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1243,a,1267,b)].
% 7.27/7.49  Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0.  [resolve(1243,a,1268,a)].
% 7.27/7.49  1269 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__ring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_38) # label(axiom).  [assumption].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A).  [resolve(1269,b,1244,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A).  [resolve(1269,b,1245,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(1269,b,1246,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1269,b,1247,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A).  [resolve(1269,b,1248,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1269,b,1249,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A).  [resolve(1269,b,1250,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A).  [resolve(1269,b,1251,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A).  [resolve(1269,b,1252,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1269,b,1253,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1269,b,1254,b)].
% 7.27/7.49  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1269,b,1255,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A).  [resolve(1269,b,1256,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A).  [resolve(1269,b,1257,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A).  [resolve(1269,b,1258,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A).  [resolve(1269,b,1259,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A).  [resolve(1269,b,1260,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1269,b,1261,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A).  [resolve(1269,b,1262,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A).  [resolve(1269,b,1263,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A).  [resolve(1269,b,1264,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A).  [resolve(1269,b,1265,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A).  [resolve(1269,b,1266,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1269,b,1267,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0.  [resolve(1269,b,1268,a)].
% 7.27/7.50  1270 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__ring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_47) # label(axiom).  [assumption].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A).  [resolve(1270,b,1244,b)].
% 7.27/7.50  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A).  [resolve(1270,b,1245,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(1270,b,1246,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1270,b,1247,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A).  [resolve(1270,b,1248,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1270,b,1249,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A).  [resolve(1270,b,1250,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A).  [resolve(1270,b,1251,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A).  [resolve(1270,b,1252,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1270,b,1253,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1270,b,1254,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1270,b,1255,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A).  [resolve(1270,b,1256,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A).  [resolve(1270,b,1257,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A).  [resolve(1270,b,1258,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A).  [resolve(1270,b,1259,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A).  [resolve(1270,b,1260,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A).  [resolve(1270,b,1261,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A).  [resolve(1270,b,1262,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A).  [resolve(1270,b,1263,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A).  [resolve(1270,b,1264,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A).  [resolve(1270,b,1265,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A).  [resolve(1270,b,1266,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A).  [resolve(1270,b,1267,b)].
% 7.27/7.51  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,C,A) != c_0 | C = c_0 | B = c_0.  [resolve(1270,b,1268,a)].
% 7.27/7.51  1271 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_1) # label(axiom).  [assumption].
% 7.27/7.51  1272 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_10) # label(axiom).  [assumption].
% 7.27/7.51  1273 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_12) # label(axiom).  [assumption].
% 7.27/7.51  1274 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_13) # label(axiom).  [assumption].
% 7.27/7.51  1275 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_14) # label(axiom).  [assumption].
% 7.27/7.51  1276 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_15) # label(axiom).  [assumption].
% 7.27/7.51  1277 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_16) # label(axiom).  [assumption].
% 7.27/7.51  1278 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom).  [assumption].
% 7.27/7.51  1279 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_2) # label(axiom).  [assumption].
% 7.27/7.51  1280 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_21) # label(axiom).  [assumption].
% 7.27/7.51  1281 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_22) # label(axiom).  [assumption].
% 7.27/7.51  1282 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_23) # label(axiom).  [assumption].
% 7.27/7.52  1283 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_24) # label(axiom).  [assumption].
% 7.27/7.52  1284 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_25) # label(axiom).  [assumption].
% 7.27/7.52  1285 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom).  [assumption].
% 7.27/7.52  1286 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom).  [assumption].
% 7.27/7.52  1287 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_28) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint).  [resolve(1287,a,1243,a)].
% 7.27/7.52  Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1287,a,1269,b)].
% 7.27/7.52  Derived: class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1287,a,1270,b)].
% 7.27/7.52  1288 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_29) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1288,a,1243,a)].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1288,a,1269,b)].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1288,a,1270,b)].
% 7.27/7.52  1289 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_30) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(1289,a,1243,a)].
% 7.27/7.52  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1289,a,1269,b)].
% 7.27/7.52  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1289,a,1270,b)].
% 7.27/7.52  1290 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_31) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint).  [resolve(1290,a,1243,a)].
% 7.27/7.52  Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1290,a,1269,b)].
% 7.27/7.52  Derived: class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1290,a,1270,b)].
% 7.27/7.52  1291 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_32) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint).  [resolve(1291,a,1243,a)].
% 7.27/7.52  Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1291,a,1269,b)].
% 7.27/7.52  Derived: class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1291,a,1270,b)].
% 7.27/7.52  1292 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_33) # label(axiom).  [assumption].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint).  [resolve(1292,a,1243,a)].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1292,a,1269,b)].
% 7.27/7.52  Derived: class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1292,a,1270,b)].
% 7.27/7.52  1293 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_34) # label(axiom).  [assumption].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint).  [resolve(1293,a,1243,a)].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1293,a,1269,b)].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1293,a,1270,b)].
% 7.36/7.55  1294 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_35) # label(axiom).  [assumption].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint).  [resolve(1294,a,1243,a)].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1294,a,1269,b)].
% 7.36/7.55  Derived: class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1294,a,1270,b)].
% 7.36/7.55  1295 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_36) # label(axiom).  [assumption].
% 7.36/7.55  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint).  [resolve(1295,a,1243,a)].
% 7.36/7.55  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1295,a,1269,b)].
% 7.36/7.55  Derived: class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1295,a,1270,b)].
% 7.36/7.55  1296 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_8) # label(axiom).  [assumption].
% 7.36/7.55  1297 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_9) # label(axiom).  [assumption].
% 7.36/7.55  1298 -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(30,b,1,a)].
% 7.36/7.55  1299 -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(30,b,3,a)].
% 7.36/7.55  1300 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(30,b,9,a)].
% 7.36/7.55  1301 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(30,b,10,a)].
% 7.36/7.55  1302 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(151,b,131,b)].
% 7.36/7.55  1303 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(151,b,133,b)].
% 7.36/7.55  1304 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(165,a,151,b)].
% 7.36/7.55  1305 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(166,a,151,b)].
% 7.36/7.55  1306 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(236,a,221,b)].
% 7.36/7.55  1307 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(237,a,221,b)].
% 7.36/7.55  1308 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(241,a,221,b)].
% 7.36/7.55  1309 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(242,a,221,b)].
% 7.36/7.55  1310 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(297,b,280,a)].
% 7.36/7.55  1311 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(297,b,282,a)].
% 7.36/7.57  1312 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(314,a,297,b)].
% 7.36/7.57  1313 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(315,a,297,b)].
% 7.36/7.57  1314 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(317,a,297,b)].
% 7.36/7.57  1315 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(318,a,297,b)].
% 7.36/7.57  1316 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(336,b,321,b)].
% 7.36/7.57  1317 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(336,b,323,b)].
% 7.36/7.57  1318 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(336,b,324,a)].
% 7.36/7.57  1319 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(336,b,325,a)].
% 7.36/7.57  1320 -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(336,b,326,a)].
% 7.36/7.57  1321 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(344,a,336,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1321,b,1269,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1321,b,1270,b)].
% 7.36/7.57  1322 class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(345,a,336,b)].
% 7.36/7.57  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1322,b,1269,b)].
% 7.36/7.57  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1322,b,1270,b)].
% 7.36/7.57  1323 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(356,b,336,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1323,b,1269,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1323,b,1270,b)].
% 7.36/7.57  1324 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(357,b,336,b)].
% 7.36/7.57  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1324,b,1269,b)].
% 7.36/7.57  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1324,b,1270,b)].
% 7.36/7.57  1325 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(358,b,336,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1325,b,1269,b)].
% 7.36/7.57  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1325,b,1270,b)].
% 7.36/7.57  1326 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(359,b,336,b)].
% 7.36/7.57  1327 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(360,c,336,b)].
% 7.36/7.57  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1327,c,1269,b)].
% 7.36/7.57  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1327,c,1270,b)].
% 7.36/7.57  1328 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A).  [resolve(361,c,336,b)].
% 7.42/7.64  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1328,c,1269,b)].
% 7.42/7.64  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1328,c,1270,b)].
% 7.42/7.64  1329 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(362,a,336,b)].
% 7.42/7.64  1330 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B).  [resolve(363,a,336,b)].
% 7.42/7.64  1331 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(364,c,336,b)].
% 7.42/7.64  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(1331,c,1269,b)].
% 7.42/7.64  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1331,c,1270,b)].
% 7.42/7.64  1332 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C).  [resolve(365,c,336,b)].
% 7.42/7.64  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(1332,c,1269,b)].
% 7.42/7.64  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1332,c,1270,b)].
% 7.42/7.64  1333 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(786,a,708,a)].
% 7.42/7.64  1334 -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A).  [resolve(786,a,715,a)].
% 7.42/7.64  1335 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(874,b,806,a)].
% 7.42/7.64  1336 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(874,b,807,a)].
% 7.42/7.64  1337 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(874,b,808,a)].
% 7.42/7.64  1338 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(874,b,809,a)].
% 7.42/7.64  1339 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,810,a)].
% 7.42/7.64  1340 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,811,a)].
% 7.42/7.64  1341 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(874,b,812,a)].
% 7.42/7.64  1342 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,813,a)].
% 7.42/7.64  1343 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(874,b,814,a)].
% 7.42/7.64  1344 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(874,b,815,a)].
% 7.42/7.64  1345 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(874,b,816,a)].
% 7.48/7.65  1346 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,817,a)].
% 7.48/7.65  1347 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,818,a)].
% 7.48/7.65  1348 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(874,b,819,a)].
% 7.48/7.65  1349 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,820,a)].
% 7.48/7.65  1350 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(874,b,821,a)].
% 7.48/7.65  1351 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(874,b,822,a)].
% 7.48/7.65  1352 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(874,b,823,a)].
% 7.48/7.65  1353 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(874,b,824,a)].
% 7.48/7.65  1354 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(874,b,825,a)].
% 7.48/7.65  1355 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(874,b,826,a)].
% 7.48/7.65  1356 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(874,b,827,a)].
% 7.48/7.65  1357 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(874,b,828,a)].
% 7.48/7.65  1358 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(874,b,829,b)].
% 7.48/7.65  1359 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(874,b,830,b)].
% 7.48/7.65  1360 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(874,b,831,a)].
% 7.48/7.65  1361 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(874,b,832,a)].
% 7.48/7.65  1362 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(874,b,833,a)].
% 7.48/7.65  1363 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(874,b,834,a)].
% 7.48/7.65  1364 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(874,b,835,a)].
% 7.48/7.65  1365 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(874,b,836,a)].
% 7.48/7.65  1366 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(874,b,837,a)].
% 7.48/7.65  1367 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(874,b,838,a)].
% 7.48/7.66  1368 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(874,b,839,a)].
% 7.48/7.66  1369 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(874,b,840,a)].
% 7.48/7.66  1370 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(874,b,841,a)].
% 7.48/7.66  1371 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(874,b,842,a)].
% 7.48/7.66  1372 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(874,b,843,a)].
% 7.48/7.66  1373 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(874,b,844,a)].
% 7.48/7.66  1374 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(874,b,845,a)].
% 7.48/7.66  1375 -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(874,b,846,a)].
% 7.48/7.66  1376 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(874,b,847,a)].
% 7.48/7.66  1377 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(874,b,848,a)].
% 7.48/7.66  1378 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(874,b,849,a)].
% 7.48/7.66  1379 -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(874,b,850,a)].
% 7.48/7.66  1380 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(874,b,851,a)].
% 7.48/7.66  1381 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(874,b,852,a)].
% 7.48/7.66  1382 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(874,b,853,a)].
% 7.48/7.66  1383 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(874,b,854,a)].
% 7.48/7.66  1384 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(874,b,855,a)].
% 7.48/7.66  1385 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(874,b,856,a)].
% 7.48/7.66  1386 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(874,b,857,a)].
% 7.48/7.66  1387 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(874,b,858,a)].
% 7.48/7.66  1388 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(874,b,859,a)].
% 7.48/7.66  1389 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(874,b,860,a)].
% 7.48/7.66  1390 -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(874,b,861,a)].
% 7.48/7.66  1391 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(874,b,862,a)].
% 7.67/7.86  1392 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(874,b,863,a)].
% 7.67/7.86  1393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1060,b,1046,a)].
% 7.67/7.86  1394 -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1083,b,1069,a)].
% 7.67/7.86  1395 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom).  [assumption].
% 7.67/7.86  1396 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0 # label(cls_OrderedGroup_Oabs__0__eq_0) # label(axiom).  [assumption].
% 7.67/7.86  1397 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 = c_HOL_Oabs(c_0,A) # label(cls_OrderedGroup_Oabs__0__eq_1) # label(axiom).  [assumption].
% 7.67/7.86  1398 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) # label(cls_OrderedGroup_Oabs__add__abs_0) # label(axiom).  [assumption].
% 7.67/7.86  1399 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0 # label(cls_OrderedGroup_Oabs__eq__0_0) # label(axiom).  [assumption].
% 7.67/7.86  1400 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_0,A) = c_0 # label(cls_OrderedGroup_Oabs__eq__0_1) # label(axiom).  [assumption].
% 7.67/7.86  1401 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom).  [assumption].
% 7.67/7.86  1402 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__idempotent_0) # label(axiom).  [assumption].
% 7.67/7.86  1403 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0 # label(cls_OrderedGroup_Oabs__le__zero__iff_0) # label(axiom).  [assumption].
% 7.67/7.86  1404 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) # label(cls_OrderedGroup_Oabs__le__zero__iff_1) # label(axiom).  [assumption].
% 7.67/7.86  1405 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__minus__cancel_0) # label(axiom).  [assumption].
% 7.67/7.86  1406 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_HOL_Oabs(B,A),c_0,A) # label(cls_OrderedGroup_Oabs__not__less__zero_0) # label(axiom).  [assumption].
% 7.67/7.86  1407 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B # label(cls_OrderedGroup_Oabs__of__nonneg_0) # label(axiom).  [assumption].
% 7.67/7.86  1408 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A) # label(cls_OrderedGroup_Oabs__of__nonpos_0) # label(axiom).  [assumption].
% 7.67/7.86  1409 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A) # label(cls_OrderedGroup_Ozero__less__abs__iff_0) # label(axiom).  [assumption].
% 7.67/7.86  1410 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0 # label(cls_OrderedGroup_Ozero__less__abs__iff_1) # label(axiom).  [assumption].
% 7.67/7.86  Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1396,a)].
% 7.67/7.86  Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint).  [resolve(1395,a,1397,a)].
% 7.67/7.86  Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1395,a,1398,a)].
% 7.67/7.86  Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1395,a,1399,a)].
% 7.67/7.86  Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0.  [resolve(1395,a,1400,a)].
% 7.67/7.86  Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1395,a,1401,a)].
% 7.67/7.86  Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint).  [resolve(1395,a,1402,a)].
% 7.67/7.86  Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1403,a)].
% 7.67/7.86  Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1395,a,1404,a)].
% 7.67/7.87  Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint).  [resolve(1395,a,1405,a)].
% 7.67/7.87  Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1395,a,1406,a)].
% 7.67/7.87  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A.  [resolve(1395,a,1407,a)].
% 7.67/7.87  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint).  [resolve(1395,a,1408,a)].
% 7.67/7.87  Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1395,a,1409,a)].
% 7.67/7.87  Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0.  [resolve(1395,a,1410,a)].
% 7.67/7.87  1411 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom).  [assumption].
% 7.67/7.87  1412 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_1) # label(axiom).  [assumption].
% 7.67/7.87  1413 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom).  [assumption].
% 7.67/7.87  1414 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom).  [assumption].
% 7.67/7.87  1415 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom).  [assumption].
% 7.67/7.87  1416 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom).  [assumption].
% 7.67/7.87  1417 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom).  [assumption].
% 7.67/7.87  1418 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom).  [assumption].
% 7.67/7.87  1419 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom).  [assumption].
% 7.67/7.87  1420 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom).  [assumption].
% 7.67/7.87  1421 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom).  [assumption].
% 7.67/7.87  1422 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_6) # label(axiom).  [assumption].
% 7.67/7.87  1423 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_7) # label(axiom).  [assumption].
% 7.67/7.87  1424 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_8) # label(axiom).  [assumption].
% 7.67/7.87  1425 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Olordered__ring_24) # label(axiom).  [assumption].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1425,b,1396,a)].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1425,b,1397,a)].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).  [resolve(1425,b,1398,a)].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1425,b,1399,a)].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1425,b,1400,a)].
% 7.67/7.87  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1425,b,1401,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1425,b,1402,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0.  [resolve(1425,b,1403,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1425,b,1404,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1425,b,1405,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1425,b,1406,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B.  [resolve(1425,b,1407,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A).  [resolve(1425,b,1408,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1425,b,1409,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0.  [resolve(1425,b,1410,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1425,b,1412,a)].
% 7.67/7.89  1426 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__field_47) # label(axiom).  [assumption].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1426,b,1396,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1426,b,1397,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).  [resolve(1426,b,1398,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1426,b,1399,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1426,b,1400,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1426,b,1401,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1426,b,1402,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0.  [resolve(1426,b,1403,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1426,b,1404,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1426,b,1405,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1426,b,1406,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B.  [resolve(1426,b,1407,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A).  [resolve(1426,b,1408,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1426,b,1409,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0.  [resolve(1426,b,1410,a)].
% 7.67/7.89  1427 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__abs(A) # label(clsrel_Ring__and__Field_Oordered__idom_50) # label(axiom).  [assumption].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1427,b,1396,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1427,b,1397,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).  [resolve(1427,b,1398,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1427,b,1399,a)].
% 7.67/7.89  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1427,b,1400,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1427,b,1401,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1427,b,1402,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0.  [resolve(1427,b,1403,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1427,b,1404,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1427,b,1405,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1427,b,1406,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B.  [resolve(1427,b,1407,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A).  [resolve(1427,b,1408,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1427,b,1409,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0.  [resolve(1427,b,1410,a)].
% 7.87/8.08  1428 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(12,b,1,a)].
% 7.87/8.08  1429 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(12,b,3,a)].
% 7.87/8.08  1430 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(50,b,47,a)].
% 7.87/8.08  1431 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A).  [resolve(50,b,48,a)].
% 7.87/8.08  1432 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1052,b,1046,a)].
% 7.87/8.08  1433 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1075,b,1069,a)].
% 7.87/8.08  1434 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint).  [resolve(1292,a,1243,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1434,a,1411,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(1434,a,1412,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1413,a)].
% 7.87/8.08  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1434,a,1414,a)].
% 7.87/8.08  Derived: class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(1434,a,1415,a)].
% 7.87/8.08  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1434,a,1416,a)].
% 7.87/8.08  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1434,a,1417,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(1434,a,1418,a)].
% 7.87/8.08  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(1434,a,1419,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(1434,a,1420,a)].
% 7.87/8.08  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(1434,a,1421,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1434,a,1422,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1423,a)].
% 7.87/8.08  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1424,a)].
% 7.87/8.08  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1434,a,1428,a)].
% 7.87/8.08  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1434,a,1429,a)].
% 7.87/8.08  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(1434,a,1432,a)].
% 7.87/8.08  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(1434,a,1433,a)].
% 7.87/8.08  1435 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1292,a,1269,b)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1435,a,1411,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1435,a,1412,a)].
% 7.87/8.08  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1435,a,1413,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1435,a,1414,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A).  [resolve(1435,a,1415,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1435,a,1416,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1435,a,1417,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A).  [resolve(1435,a,1421,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1435,a,1422,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1435,a,1423,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1435,a,1424,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1435,a,1432,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1435,a,1433,a)].
% 8.02/8.19  1436 class_OrderedGroup_Olordered__ab__group__abs(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1292,a,1270,b)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1436,a,1411,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1436,a,1412,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1436,a,1413,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1436,a,1414,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A).  [resolve(1436,a,1415,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1436,a,1416,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1436,a,1417,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A).  [resolve(1436,a,1421,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1436,a,1422,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1436,a,1423,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1436,a,1424,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1436,a,1432,a)].
% 8.02/8.19  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1436,a,1433,a)].
% 8.02/8.19  1437 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom).  [assumption].
% 8.02/8.19  1438 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__left_0) # label(axiom).  [assumption].
% 8.02/8.19  1439 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__left_1) # label(axiom).  [assumption].
% 8.02/8.19  1440 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__right_0) # label(axiom).  [assumption].
% 8.02/8.19  1441 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__right_1) # label(axiom).  [assumption].
% 8.02/8.19  1442 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__left_0) # label(axiom).  [assumption].
% 8.02/8.20  1443 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__left_1) # label(axiom).  [assumption].
% 8.02/8.20  1444 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__right_0) # label(axiom).  [assumption].
% 8.02/8.20  1445 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__right_1) # label(axiom).  [assumption].
% 8.02/8.20  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(1437,a,1438,a)].
% 8.02/8.20  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1437,a,1439,a)].
% 8.02/8.20  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1437,a,1440,a)].
% 8.02/8.20  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1437,a,1441,a)].
% 8.02/8.20  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(1437,a,1442,a)].
% 8.02/8.20  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1437,a,1443,a)].
% 8.02/8.20  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1437,a,1444,a)].
% 8.02/8.20  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1437,a,1445,a)].
% 8.02/8.20  1446 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom).  [assumption].
% 8.02/8.20  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(1446,a,1438,a)].
% 8.02/8.20  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(1446,a,1439,a)].
% 8.02/8.20  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1446,a,1440,a)].
% 8.02/8.20  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(1446,a,1441,a)].
% 8.02/8.20  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat).  [resolve(1446,a,1442,a)].
% 8.02/8.20  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(1446,a,1443,a)].
% 8.02/8.20  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1446,a,1444,a)].
% 8.02/8.20  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(1446,a,1445,a)].
% 8.02/8.20  1447 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group_5) # label(axiom).  [assumption].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1447,b,1438,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1447,b,1439,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1447,b,1440,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1447,b,1441,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1447,b,1442,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1447,b,1443,a)].
% 8.02/8.20  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1447,b,1444,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1447,b,1445,a)].
% 8.02/8.21  1448 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_5) # label(axiom).  [assumption].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1448,b,1438,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1448,b,1439,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1448,b,1440,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1448,b,1441,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1448,b,1442,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1448,b,1443,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1448,b,1444,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1448,b,1445,a)].
% 8.02/8.21  1449 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_5) # label(axiom).  [assumption].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1449,b,1438,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1449,b,1439,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1449,b,1440,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1449,b,1441,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1449,b,1442,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1449,b,1443,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1449,b,1444,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1449,b,1445,a)].
% 8.02/8.21  1450 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) # label(axiom).  [assumption].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1450,b,1438,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1450,b,1439,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1450,b,1440,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1450,b,1441,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1450,b,1442,a)].
% 8.02/8.21  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1450,b,1443,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1450,b,1444,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1450,b,1445,a)].
% 8.02/8.22  1451 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_12) # label(axiom).  [assumption].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1451,b,1438,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1451,b,1439,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1451,b,1440,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1451,b,1441,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1451,b,1442,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1451,b,1443,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1451,b,1444,a)].
% 8.02/8.22  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1451,b,1445,a)].
% 8.02/8.22  1452 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) # label(axiom).  [assumption].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1452,a,1447,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1452,a,1448,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1452,a,1449,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1452,a,1450,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1452,a,1451,b)].
% 8.02/8.22  1453 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) # label(axiom).  [assumption].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1453,a,1447,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1453,a,1448,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1453,a,1449,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1453,a,1450,b)].
% 8.02/8.22  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1453,a,1451,b)].
% 8.02/8.22  1454 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) # label(axiom).  [assumption].
% 8.02/8.22  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1454,a,1447,b)].
% 8.02/8.22  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1454,a,1448,b)].
% 8.02/8.23  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1454,a,1449,b)].
% 8.02/8.23  Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1454,a,1451,b)].
% 8.02/8.23  1455 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) # label(axiom).  [assumption].
% 8.02/8.23  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1455,a,1447,b)].
% 8.02/8.23  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1455,a,1448,b)].
% 8.02/8.23  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1455,a,1449,b)].
% 8.02/8.23  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1455,a,1451,b)].
% 8.02/8.23  1456 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) # label(axiom).  [assumption].
% 8.02/8.23  1457 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) # label(axiom).  [assumption].
% 8.02/8.23  1458 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Olordered__ring_5) # label(axiom).  [assumption].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1458,b,1438,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1458,b,1439,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1458,b,1440,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1458,b,1441,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1458,b,1442,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1458,b,1443,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1458,b,1444,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1458,b,1445,a)].
% 8.02/8.23  1459 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) # label(axiom).  [assumption].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1459,b,1438,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1459,b,1439,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1459,b,1440,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1459,b,1441,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1459,b,1442,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1459,b,1443,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1459,b,1444,a)].
% 8.02/8.23  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1459,b,1445,a)].
% 8.02/8.24  1460 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__field_55) # label(axiom).  [assumption].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1460,b,1438,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1460,b,1439,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1460,b,1440,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1460,b,1441,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1460,b,1442,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1460,b,1443,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1460,b,1444,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1460,b,1445,a)].
% 8.02/8.24  1461 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__idom_37) # label(axiom).  [assumption].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1461,b,1438,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1461,b,1439,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1461,b,1440,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1461,b,1441,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1461,b,1442,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1461,b,1443,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1461,b,1444,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1461,b,1445,a)].
% 8.02/8.24  1462 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_14) # label(axiom).  [assumption].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1462,b,1438,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1462,b,1439,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1462,b,1440,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1462,b,1441,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1462,b,1442,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1462,b,1443,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1462,b,1444,a)].
% 8.02/8.24  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1462,b,1445,a)].
% 8.10/8.26  1463 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # label(clsrel_Ring__and__Field_Opordered__ring_20) # label(axiom).  [assumption].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1463,b,1438,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1463,b,1439,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1463,b,1440,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1463,b,1441,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1463,b,1442,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1463,b,1443,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1463,b,1444,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1463,b,1445,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1463,b,1453,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1463,b,1454,a)].
% 8.10/8.26  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A).  [resolve(1463,b,1455,a)].
% 8.10/8.26  1464 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(17,b,1,a)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1464,a,1447,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1464,a,1448,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1464,a,1449,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1464,a,1450,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1464,a,1451,b)].
% 8.10/8.26  1465 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(17,b,3,a)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1465,a,1447,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1465,a,1448,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1465,a,1449,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1465,a,1450,b)].
% 8.10/8.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1465,a,1451,b)].
% 8.10/8.26  1466 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(81,b,55,b)].
% 8.10/8.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1466,b,1447,b)].
% 8.10/8.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1466,b,1448,b)].
% 8.10/8.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1466,b,1449,b)].
% 8.10/8.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1466,b,1450,b)].
% 8.10/8.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1466,b,1451,b)].
% 8.10/8.26  1467 class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(82,b,55,b)].
% 8.41/8.58  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1467,b,1447,b)].
% 8.41/8.58  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1467,b,1448,b)].
% 8.41/8.58  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1467,b,1449,b)].
% 8.41/8.58  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1467,b,1450,b)].
% 8.41/8.58  Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1467,b,1451,b)].
% 8.41/8.58  1468 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1130,a,1091,a)].
% 8.41/8.58  1469 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).  [resolve(1130,a,1116,a)].
% 8.41/8.58  Derived: class_Orderings_Oorder(tc_nat).  [resolve(1469,a,1454,a)].
% 8.41/8.58  Derived: class_Orderings_Oord(tc_nat).  [resolve(1469,a,1455,a)].
% 8.41/8.58  Derived: class_HOL_Oplus(tc_nat).  [resolve(1469,a,1457,a)].
% 8.41/8.58  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(1469,a,1464,a)].
% 8.41/8.58  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(1469,a,1465,a)].
% 8.41/8.58  1470 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1130,a,1117,b)].
% 8.41/8.58  1471 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1130,a,1118,b)].
% 8.41/8.58  1472 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint).  [resolve(1434,a,1422,a)].
% 8.41/8.58  Derived: class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1472,a,1454,a)].
% 8.41/8.58  Derived: class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1472,a,1455,a)].
% 8.41/8.58  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1472,a,1456,a)].
% 8.41/8.58  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1472,a,1457,a)].
% 8.41/8.58  1473 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1435,a,1422,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1473,b,1454,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1473,b,1455,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1473,b,1456,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1473,b,1457,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(1473,b,1464,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(1473,b,1465,a)].
% 8.41/8.58  1474 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).  [resolve(1436,a,1422,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1474,b,1454,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1474,b,1455,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1474,b,1456,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1474,b,1457,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(1474,b,1464,a)].
% 8.41/8.58  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(1474,b,1465,a)].
% 8.41/8.58  1475 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom).  [assumption].
% 8.41/8.58  1476 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) # label(axiom).  [assumption].
% 8.41/8.58  1477 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) # label(axiom).  [assumption].
% 8.41/8.58  1478 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1479 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_1) # label(axiom).  [assumption].
% 8.41/8.58  1480 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1481 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_1) # label(axiom).  [assumption].
% 8.41/8.58  1482 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__join__eq__meet_0) # label(axiom).  [assumption].
% 8.41/8.58  1483 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__meet__eq__join_0) # label(axiom).  [assumption].
% 8.41/8.58  1484 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1485 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0 # label(cls_OrderedGroup_Onprt__eq__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1486 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B # label(cls_OrderedGroup_Onprt__eq__id_0) # label(axiom).  [assumption].
% 8.41/8.58  1487 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A) # label(cls_OrderedGroup_Onprt__le__zero_0) # label(axiom).  [assumption].
% 8.41/8.58  1488 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A) # label(cls_OrderedGroup_Onprt__mono_0) # label(axiom).  [assumption].
% 8.41/8.58  1489 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1490 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0 # label(cls_OrderedGroup_Opprt__eq__0_0) # label(axiom).  [assumption].
% 8.41/8.58  1491 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B # label(cls_OrderedGroup_Opprt__eq__id_0) # label(axiom).  [assumption].
% 8.41/8.58  1492 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A) # label(cls_OrderedGroup_Opprt__mono_0) # label(axiom).  [assumption].
% 8.41/8.58  1493 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) # label(axiom).  [assumption].
% 8.41/8.58  1494 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) # label(axiom).  [assumption].
% 8.41/8.58  1495 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A) # label(cls_OrderedGroup_Ozero__le__pprt_0) # label(axiom).  [assumption].
% 8.41/8.58  Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint).  [resolve(1475,a,1476,a)].
% 8.41/8.58  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1475,a,1477,a)].
% 8.41/8.58  Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1475,a,1478,a)].
% 8.41/8.58  Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(1475,a,1479,a)].
% 8.41/8.58  Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(1475,a,1480,a)].
% 8.41/8.58  Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(1475,a,1481,a)].
% 8.41/8.58  Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1482,a)].
% 8.41/8.59  Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1483,a)].
% 8.41/8.59  Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1484,a)].
% 8.41/8.59  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1485,a)].
% 8.41/8.59  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A.  [resolve(1475,a,1486,a)].
% 8.41/8.59  Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(1475,a,1487,a)].
% 8.41/8.59  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1488,a)].
% 8.41/8.59  Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1489,a)].
% 8.41/8.59  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0.  [resolve(1475,a,1490,a)].
% 8.41/8.59  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A.  [resolve(1475,a,1491,a)].
% 8.41/8.59  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1492,a)].
% 8.41/8.59  Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint).  [resolve(1475,a,1493,a)].
% 8.41/8.59  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1494,a)].
% 8.41/8.59  Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1475,a,1495,a)].
% 8.41/8.59  1496 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom).  [assumption].
% 8.41/8.59  1497 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom).  [assumption].
% 8.41/8.59  1498 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom).  [assumption].
% 8.41/8.59  1499 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom).  [assumption].
% 8.41/8.59  1500 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom).  [assumption].
% 8.41/8.59  1501 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom).  [assumption].
% 8.41/8.59  1502 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom).  [assumption].
% 8.41/8.59  1503 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom).  [assumption].
% 8.41/8.59  1504 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom).  [assumption].
% 8.41/8.59  1505 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom).  [assumption].
% 8.41/8.59  1506 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom).  [assumption].
% 8.41/8.59  1507 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom).  [assumption].
% 8.41/8.59  1508 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom).  [assumption].
% 8.41/8.59  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1508,b,1476,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1508,b,1477,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1508,b,1478,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1508,b,1479,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1508,b,1480,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1508,b,1481,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1508,b,1482,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1508,b,1483,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1508,b,1484,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1508,b,1485,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1508,b,1486,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1508,b,1487,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1508,b,1488,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1508,b,1489,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1508,b,1490,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1508,b,1491,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1508,b,1492,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1508,b,1493,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1508,b,1494,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1508,b,1495,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1508,b,1496,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1508,b,1497,a)].
% 8.44/8.60  1509 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom).  [assumption].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1509,b,1476,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1509,b,1477,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1509,b,1478,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1509,b,1479,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1509,b,1480,a)].
% 8.44/8.60  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1509,b,1481,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1509,b,1482,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1509,b,1483,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1509,b,1484,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1509,b,1485,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1509,b,1486,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1509,b,1487,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1509,b,1488,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1509,b,1489,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1509,b,1490,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1509,b,1491,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1509,b,1492,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1509,b,1493,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1509,b,1494,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1509,b,1495,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1509,b,1496,a)].
% 8.44/8.61  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1509,b,1497,a)].
% 8.44/8.61  1510 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom).  [assumption].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1510,b,1476,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1510,b,1477,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1510,b,1478,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1510,b,1479,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1510,b,1480,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1510,b,1481,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1510,b,1482,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1510,b,1483,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1510,b,1484,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1510,b,1485,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1510,b,1486,a)].
% 8.44/8.61  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1510,b,1487,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1510,b,1488,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1510,b,1489,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1510,b,1490,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1510,b,1491,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1510,b,1492,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1510,b,1493,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1510,b,1494,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1510,b,1495,a)].
% 8.46/8.63  1511 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom).  [assumption].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1511,b,1476,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1511,b,1477,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1511,b,1478,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1511,b,1479,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1511,b,1480,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1511,b,1481,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1511,b,1482,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1511,b,1483,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1511,b,1484,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1511,b,1485,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1511,b,1486,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1511,b,1487,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1511,b,1488,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1511,b,1489,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1511,b,1490,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1511,b,1491,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1511,b,1492,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1511,b,1493,a)].
% 8.46/8.63  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1511,b,1494,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1511,b,1495,a)].
% 8.64/8.84  1512 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom).  [assumption].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1512,b,1476,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1512,b,1477,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1512,b,1478,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1512,b,1479,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1512,b,1480,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1512,b,1481,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1512,b,1482,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1512,b,1483,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1512,b,1484,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1512,b,1485,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1512,b,1486,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1512,b,1487,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1512,b,1488,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1512,b,1489,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1512,b,1490,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1512,b,1491,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1512,b,1492,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1512,b,1493,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1512,b,1494,a)].
% 8.64/8.84  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1512,b,1495,a)].
% 8.64/8.84  1513 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(11,b,1,a)].
% 8.64/8.84  1514 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(11,b,3,a)].
% 8.64/8.84  1515 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(81,b,49,b)].
% 8.64/8.84  1516 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(82,b,49,b)].
% 8.64/8.84  1517 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1051,b,1046,a)].
% 8.64/8.84  1518 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1074,b,1069,a)].
% 8.64/8.84  1519 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1288,a,1243,a)].
% 8.64/8.84  1520 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1288,a,1269,b)].
% 8.64/8.84  1521 class_OrderedGroup_Olordered__ab__group(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1288,a,1270,b)].
% 8.64/8.84  1522 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint).  [resolve(1434,a,1411,a)].
% 8.64/8.85  1523 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1435,a,1411,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1523,b,1497,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ominus(A).  [resolve(1523,b,1501,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(1523,b,1502,a)].
% 8.64/8.85  1524 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A).  [resolve(1436,a,1411,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1524,b,1497,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A).  [resolve(1524,b,1501,a)].
% 8.64/8.85  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A).  [resolve(1524,b,1502,a)].
% 8.64/8.85  1525 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1447,b,1438,a)].
% 8.64/8.85  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(1525,a,1475,a)].
% 8.64/8.85  1526 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1447,b,1439,a)].
% 8.64/8.85  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1526,a,1475,a)].
% 8.64/8.85  1527 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1447,b,1440,a)].
% 8.64/8.85  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1527,a,1475,a)].
% 8.64/8.85  1528 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1447,b,1441,a)].
% 8.64/8.85  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1528,a,1475,a)].
% 8.64/8.85  1529 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1447,b,1442,a)].
% 8.64/8.85  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(1529,a,1475,a)].
% 8.64/8.85  1530 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1447,b,1443,a)].
% 8.64/8.85  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1530,a,1475,a)].
% 8.64/8.85  1531 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1447,b,1444,a)].
% 8.64/8.85  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1531,a,1475,a)].
% 8.64/8.85  1532 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1447,b,1445,a)].
% 8.64/8.85  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1532,a,1475,a)].
% 8.64/8.85  1533 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1452,a,1447,b)].
% 8.64/8.85  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1533,b,1475,a)].
% 8.64/8.85  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1533,b,1510,b)].
% 8.64/8.85  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1533,b,1511,b)].
% 8.64/8.85  Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1533,b,1512,b)].
% 8.64/8.85  1534 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1453,a,1447,b)].
% 8.78/8.98  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1534,b,1475,a)].
% 8.78/8.98  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1534,b,1510,b)].
% 8.78/8.98  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1534,b,1511,b)].
% 8.78/8.98  Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1534,b,1512,b)].
% 8.78/8.98  1535 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1454,a,1447,b)].
% 8.78/8.98  Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1535,b,1510,b)].
% 8.78/8.98  1536 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1455,a,1447,b)].
% 8.78/8.98  Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1536,b,1510,b)].
% 8.78/8.98  1537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1464,a,1447,b)].
% 8.78/8.98  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(1537,c,1475,a)].
% 8.78/8.98  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(1537,c,1510,b)].
% 8.78/8.98  1538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C).  [resolve(1465,a,1447,b)].
% 8.78/8.98  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(1538,c,1475,a)].
% 8.78/8.98  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(1538,c,1510,b)].
% 8.78/8.98  1539 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1466,b,1447,b)].
% 8.78/8.98  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1539,b,1510,b)].
% 8.78/8.98  1540 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A).  [resolve(1467,b,1447,b)].
% 8.78/8.98  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1540,b,1510,b)].
% 8.78/8.98  1541 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom).  [assumption].
% 8.78/8.98  1542 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom).  [assumption].
% 8.78/8.98  1543 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastAtMost__empty_0) # label(axiom).  [assumption].
% 8.78/8.98  1544 -class_Orderings_Oorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_OatLeastAtMost__singleton_0) # label(axiom).  [assumption].
% 8.78/8.98  1545 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastLessThan__empty_0) # label(axiom).  [assumption].
% 8.78/8.98  1546 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__subset__iff_0) # label(axiom).  [assumption].
% 8.78/8.98  1547 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)) # label(cls_SetInterval_OatLeast__subset__iff_1) # label(axiom).  [assumption].
% 8.78/8.98  1548 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__subset__iff_0) # label(axiom).  [assumption].
% 8.78/8.98  1549 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) # label(cls_SetInterval_OatMost__subset__iff_1) # label(axiom).  [assumption].
% 8.78/8.98  1550 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OgreaterThanAtMost__empty_0) # label(axiom).  [assumption].
% 8.78/8.98  1551 -class_Orderings_Oorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_Osingle__Diff__lessThan_0) # label(axiom).  [assumption].
% 8.78/8.99  1552 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom).  [assumption].
% 8.78/8.99  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1541,a,1542,a)].
% 8.78/8.99  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1543,a)].
% 8.78/8.99  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1541,a,1544,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1545,a)].
% 8.78/8.99  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1541,a,1546,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1541,a,1547,a)].
% 8.78/8.99  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1541,a,1548,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1541,a,1549,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1541,a,1550,a)].
% 8.78/8.99  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1541,a,1551,a)].
% 8.78/8.99  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1541,a,1552,a)].
% 8.78/8.99  1553 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom).  [assumption].
% 8.78/8.99  Derived: -c_less(A,A,tc_nat).  [resolve(1553,a,1542,a)].
% 8.78/8.99  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1543,a)].
% 8.78/8.99  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1553,a,1544,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1545,a)].
% 8.78/8.99  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(1553,a,1546,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(1553,a,1547,a)].
% 8.78/8.99  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(1553,a,1548,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(1553,a,1549,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1553,a,1550,a)].
% 8.78/8.99  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(1553,a,1551,a)].
% 8.78/8.99  Derived: c_lessequals(A,A,tc_nat).  [resolve(1553,a,1552,a)].
% 8.78/8.99  1554 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom).  [assumption].
% 8.78/8.99  Derived: -c_less(A,A,tc_set(B)).  [resolve(1554,a,1542,a)].
% 8.78/8.99  Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1543,a)].
% 8.78/8.99  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)).  [resolve(1554,a,1544,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1545,a)].
% 8.78/8.99  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_set(B)),c_SetInterval_OatLeast(C,tc_set(B)),tc_set(tc_set(B))) | c_lessequals(C,A,tc_set(B)).  [resolve(1554,a,1546,a)].
% 8.78/8.99  Derived: -c_lessequals(A,B,tc_set(C)) | c_lessequals(c_SetInterval_OatLeast(B,tc_set(C)),c_SetInterval_OatLeast(A,tc_set(C)),tc_set(tc_set(C))).  [resolve(1554,a,1547,a)].
% 8.78/9.01  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_set(B)),c_SetInterval_OatMost(C,tc_set(B)),tc_set(tc_set(B))) | c_lessequals(A,C,tc_set(B)).  [resolve(1554,a,1548,a)].
% 8.78/9.01  Derived: -c_lessequals(A,B,tc_set(C)) | c_lessequals(c_SetInterval_OatMost(A,tc_set(C)),c_SetInterval_OatMost(B,tc_set(C)),tc_set(tc_set(C))).  [resolve(1554,a,1549,a)].
% 8.78/9.01  Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset.  [resolve(1554,a,1550,a)].
% 8.78/9.01  Derived: c_minus(c_insert(A,c_emptyset,tc_set(B)),c_SetInterval_OlessThan(A,tc_set(B)),tc_set(tc_set(B))) = c_insert(A,c_emptyset,tc_set(B)).  [resolve(1554,a,1551,a)].
% 8.78/9.01  Derived: c_lessequals(A,A,tc_set(B)).  [resolve(1554,a,1552,a)].
% 8.78/9.01  1555 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom).  [assumption].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A).  [resolve(1555,b,1542,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1543,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1544,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1555,b,1545,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1555,b,1546,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1555,b,1547,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1555,b,1548,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1555,b,1549,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1550,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1551,a)].
% 8.78/9.01  Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A).  [resolve(1555,b,1552,a)].
% 8.78/9.01  1556 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom).  [assumption].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A).  [resolve(1556,b,1542,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1556,b,1543,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1556,b,1544,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1556,b,1545,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1556,b,1546,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1556,b,1547,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1556,b,1548,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1556,b,1549,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1556,b,1550,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1556,b,1551,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A).  [resolve(1556,b,1552,a)].
% 8.78/9.01  1557 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom).  [assumption].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A).  [resolve(1557,b,1542,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1557,b,1543,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1557,b,1544,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1557,b,1545,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1557,b,1546,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1557,b,1547,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1557,b,1548,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1557,b,1549,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1557,b,1550,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1557,b,1551,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A).  [resolve(1557,b,1552,a)].
% 8.78/9.01  1558 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom).  [assumption].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1558,b,1542,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1558,b,1543,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1558,b,1544,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1558,b,1545,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1558,b,1546,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1558,b,1547,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1558,b,1548,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1558,b,1549,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1558,b,1550,a)].
% 8.78/9.01  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1558,b,1551,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1558,b,1552,a)].
% 8.78/9.02  1559 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom).  [assumption].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A).  [resolve(1559,b,1542,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1559,b,1543,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1559,b,1544,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1559,b,1545,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1559,b,1546,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1559,b,1547,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1559,b,1548,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1559,b,1549,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1559,b,1550,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1559,b,1551,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A).  [resolve(1559,b,1552,a)].
% 8.78/9.02  1560 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom).  [assumption].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1560,b,1542,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1560,b,1543,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1560,b,1544,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1560,b,1545,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1560,b,1546,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1560,b,1547,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1560,b,1548,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1560,b,1549,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1560,b,1550,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1560,b,1551,a)].
% 8.78/9.02  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1560,b,1552,a)].
% 8.88/9.04  1561 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom).  [assumption].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1561,b,1542,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1561,b,1543,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1561,b,1544,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1561,b,1545,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1561,b,1546,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1561,b,1547,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1561,b,1548,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1561,b,1549,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1561,b,1550,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1561,b,1551,a)].
% 8.88/9.04  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1561,b,1552,a)].
% 8.88/9.04  1562 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom).  [assumption].
% 8.88/9.04  Derived: class_Orderings_Oord(tc_set(A)).  [resolve(1562,a,1554,a)].
% 8.88/9.04  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1562,a,1560,b)].
% 8.88/9.04  Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1562,a,1561,b)].
% 8.88/9.04  1563 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom).  [assumption].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A).  [resolve(1563,b,1542,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1563,b,1543,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1563,b,1544,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1563,b,1545,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1563,b,1546,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1563,b,1547,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1563,b,1548,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1563,b,1549,a)].
% 8.88/9.04  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1563,b,1550,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1563,b,1551,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A).  [resolve(1563,b,1552,a)].
% 8.88/9.05  1564 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) # label(axiom).  [assumption].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A).  [resolve(1564,b,1542,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1564,b,1543,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1564,b,1544,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1564,b,1545,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1564,b,1546,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1564,b,1547,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1564,b,1548,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1564,b,1549,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1564,b,1550,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1564,b,1551,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1564,b,1552,a)].
% 8.88/9.05  1565 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom).  [assumption].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A).  [resolve(1565,b,1542,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1565,b,1543,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1565,b,1544,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1565,b,1545,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1565,b,1546,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1565,b,1547,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1565,b,1548,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1565,b,1549,a)].
% 8.88/9.05  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1565,b,1550,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__field(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1565,b,1551,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A).  [resolve(1565,b,1552,a)].
% 8.88/9.06  1566 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom).  [assumption].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A).  [resolve(1566,b,1542,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1566,b,1543,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1566,b,1544,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1566,b,1545,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1566,b,1546,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1566,b,1547,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1566,b,1548,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1566,b,1549,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1566,b,1550,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1566,b,1551,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A).  [resolve(1566,b,1552,a)].
% 8.88/9.06  1567 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom).  [assumption].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A).  [resolve(1567,b,1542,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1567,b,1543,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1567,b,1544,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1567,b,1545,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1567,b,1546,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1567,b,1547,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1567,b,1548,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1567,b,1549,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1567,b,1550,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1567,b,1551,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1567,b,1552,a)].
% 8.88/9.06  1568 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) # label(axiom).  [assumption].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A).  [resolve(1568,b,1542,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1568,b,1543,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1568,b,1544,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1568,b,1545,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1568,b,1546,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1568,b,1547,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1568,b,1548,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1568,b,1549,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1568,b,1550,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1568,b,1551,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1568,b,1552,a)].
% 8.88/9.06  1569 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom).  [assumption].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A).  [resolve(1569,b,1542,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1569,b,1543,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1569,b,1544,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1569,b,1545,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1569,b,1546,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1569,b,1547,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1569,b,1548,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1569,b,1549,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1569,b,1550,a)].
% 8.88/9.06  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1569,b,1551,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A).  [resolve(1569,b,1552,a)].
% 8.88/9.07  1570 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom).  [assumption].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A).  [resolve(1570,b,1542,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1570,b,1543,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1570,b,1544,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1570,b,1545,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1570,b,1546,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1570,b,1547,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1570,b,1548,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1570,b,1549,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1570,b,1550,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1570,b,1551,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A).  [resolve(1570,b,1552,a)].
% 8.88/9.07  1571 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom).  [assumption].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A).  [resolve(1571,b,1542,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1571,b,1543,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1571,b,1544,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1571,b,1545,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1571,b,1546,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1571,b,1547,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1571,b,1548,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1571,b,1549,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1571,b,1550,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1571,b,1551,a)].
% 8.88/9.07  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1571,b,1552,a)].
% 8.88/9.08  1572 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom).  [assumption].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A).  [resolve(1572,b,1542,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1572,b,1543,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1572,b,1544,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1572,b,1545,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1572,b,1546,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1572,b,1547,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1572,b,1548,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1572,b,1549,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1572,b,1550,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1572,b,1551,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A).  [resolve(1572,b,1552,a)].
% 8.88/9.08  1573 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom).  [assumption].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A).  [resolve(1573,b,1542,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1573,b,1543,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1573,b,1544,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1573,b,1545,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1573,b,1546,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1573,b,1547,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1573,b,1548,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1573,b,1549,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1573,b,1550,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1573,b,1551,a)].
% 8.88/9.08  Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A).  [resolve(1573,b,1552,a)].
% 8.88/9.08  1574 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom).  [assumption].
% 8.88/9.08  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A).  [resolve(1574,b,1542,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1543,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1544,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1574,b,1545,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1574,b,1546,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1574,b,1547,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1574,b,1548,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1574,b,1549,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1550,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1551,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A).  [resolve(1574,b,1552,a)].
% 9.26/9.47  1575 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(870,a,805,a)].
% 9.26/9.47  1576 class_Orderings_Oorder(tc_nat).  [resolve(870,a,864,a)].
% 9.26/9.47  1577 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(870,a,865,b)].
% 9.26/9.47  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A).  [resolve(1577,a,1562,a)].
% 9.26/9.47  1578 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A).  [resolve(877,b,870,a)].
% 9.26/9.47  Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(1578,b,1562,a)].
% 9.26/9.47  1579 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A).  [resolve(1050,b,1049,a)].
% 9.26/9.47  Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1579,b,1562,a)].
% 9.26/9.47  1580 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1056,b,1049,a)].
% 9.26/9.47  1581 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1137,a,1117,b)].
% 9.26/9.47  1582 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1137,a,1118,b)].
% 9.26/9.47  1583 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1434,a,1416,a)].
% 9.26/9.47  1584 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1435,a,1416,a)].
% 9.26/9.47  1585 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1436,a,1416,a)].
% 9.26/9.47  1586 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1454,a,1448,b)].
% 9.26/9.47  1587 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1454,a,1449,b)].
% 9.26/9.47  1588 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1454,a,1451,b)].
% 9.26/9.47  1589 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A).  [resolve(1463,b,1454,a)].
% 9.26/9.47  1590 class_Orderings_Oorder(tc_nat).  [resolve(1469,a,1454,a)].
% 9.26/9.47  1591 class_Orderings_Oorder(tc_IntDef_Oint).  [resolve(1472,a,1454,a)].
% 9.26/9.47  1592 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A).  [resolve(1473,b,1454,a)].
% 9.26/9.47  1593 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A).  [resolve(1474,b,1454,a)].
% 9.26/9.47  1594 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1535,b,1510,b)].
% 9.26/9.47  1595 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom).  [assumption].
% 9.26/9.47  1596 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastAtMost__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1597 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OatLeastAtMost__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1598 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A) # label(cls_SetInterval_OatLeastAtMost__iff_2) # label(axiom).  [assumption].
% 9.26/9.47  1599 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastLessThan__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1600 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OatLeastLessThan__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1601 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A) # label(cls_SetInterval_OatLeastLessThan__iff_2) # label(axiom).  [assumption].
% 9.26/9.47  1602 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1603 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A) # label(cls_SetInterval_OatLeast__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1604 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1605 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A) # label(cls_SetInterval_OatMost__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1606 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1607 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1608 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A) # label(cls_SetInterval_OgreaterThanAtMost__iff_2) # label(axiom).  [assumption].
% 9.26/9.47  1609 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1610 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1611 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A) # label(cls_SetInterval_OgreaterThanLessThan__iff_2) # label(axiom).  [assumption].
% 9.26/9.47  1612 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThan__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1613 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A) # label(cls_SetInterval_OgreaterThan__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  1614 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A) # label(cls_SetInterval_OlessThan__iff_0) # label(axiom).  [assumption].
% 9.26/9.47  1615 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A) # label(cls_SetInterval_OlessThan__iff_1) # label(axiom).  [assumption].
% 9.26/9.47  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1595,a,1596,a)].
% 9.26/9.47  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1595,a,1597,a)].
% 9.26/9.47  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1598,a)].
% 9.26/9.47  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1595,a,1599,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1595,a,1600,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1601,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1595,a,1602,a)].
% 9.32/9.48  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1603,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1595,a,1604,a)].
% 9.32/9.48  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1605,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1595,a,1606,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1595,a,1607,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1608,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1595,a,1609,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1595,a,1610,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1611,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1595,a,1612,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1613,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(1595,a,1614,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1595,a,1615,a)].
% 9.32/9.48  1616 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom).  [assumption].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1596,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1616,a,1597,a)].
% 9.32/9.48  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(1616,a,1598,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1599,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1616,a,1600,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(1616,a,1601,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1616,a,1602,a)].
% 9.32/9.48  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1616,a,1603,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1616,a,1604,a)].
% 9.32/9.48  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1616,a,1605,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1606,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1616,a,1607,a)].
% 9.32/9.48  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(1616,a,1608,a)].
% 9.32/9.48  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1609,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1616,a,1610,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(1616,a,1611,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1616,a,1612,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1616,a,1613,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1616,a,1614,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1616,a,1615,a)].
% 9.32/9.49  1617 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom).  [assumption].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)).  [resolve(1617,a,1596,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)).  [resolve(1617,a,1597,a)].
% 9.32/9.49  Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,tc_set(C)),tc_set(C)).  [resolve(1617,a,1598,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)).  [resolve(1617,a,1599,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)).  [resolve(1617,a,1600,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,tc_set(C)),tc_set(C)).  [resolve(1617,a,1601,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)).  [resolve(1617,a,1602,a)].
% 9.32/9.49  Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)).  [resolve(1617,a,1603,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)).  [resolve(1617,a,1604,a)].
% 9.32/9.49  Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)).  [resolve(1617,a,1605,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)).  [resolve(1617,a,1606,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)).  [resolve(1617,a,1607,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(B,D,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,tc_set(C)),tc_set(C)).  [resolve(1617,a,1608,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)).  [resolve(1617,a,1609,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)).  [resolve(1617,a,1610,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_set(C)) | -c_less(D,A,tc_set(C)) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,tc_set(C)),tc_set(C)).  [resolve(1617,a,1611,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)).  [resolve(1617,a,1612,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)).  [resolve(1617,a,1613,a)].
% 9.32/9.49  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)).  [resolve(1617,a,1614,a)].
% 9.32/9.49  Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)).  [resolve(1617,a,1615,a)].
% 9.32/9.49  1618 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom).  [assumption].
% 9.32/9.49  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1596,a)].
% 9.32/9.49  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1618,b,1597,a)].
% 9.32/9.49  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1618,b,1598,a)].
% 9.32/9.49  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1599,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1618,b,1600,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1618,b,1601,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1602,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1618,b,1603,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1618,b,1604,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1618,b,1605,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1618,b,1606,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1618,b,1607,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1618,b,1608,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1618,b,1609,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1618,b,1610,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1618,b,1611,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1618,b,1612,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1618,b,1613,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1618,b,1614,a)].
% 9.32/9.51  Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1618,b,1615,a)].
% 9.32/9.51  1619 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom).  [assumption].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1596,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1619,b,1597,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1619,b,1598,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1599,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1619,b,1600,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1619,b,1601,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1602,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1619,b,1603,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1619,b,1604,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1619,b,1605,a)].
% 9.32/9.51  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1619,b,1606,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1619,b,1607,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1619,b,1608,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1619,b,1609,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1619,b,1610,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1619,b,1611,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1619,b,1612,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1619,b,1613,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1619,b,1614,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1619,b,1615,a)].
% 9.32/9.52  1620 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom).  [assumption].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1596,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1620,b,1597,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1620,b,1598,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1599,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1620,b,1600,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1620,b,1601,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1602,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1620,b,1603,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1620,b,1604,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1620,b,1605,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1620,b,1606,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1620,b,1607,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1620,b,1608,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1620,b,1609,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1620,b,1610,a)].
% 9.32/9.52  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1620,b,1611,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1620,b,1612,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1620,b,1613,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1620,b,1614,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1620,b,1615,a)].
% 9.32/9.53  1621 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom).  [assumption].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1596,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1621,b,1597,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1621,b,1598,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1599,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1621,b,1600,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1621,b,1601,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1602,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1621,b,1603,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1621,b,1604,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1621,b,1605,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1621,b,1606,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1621,b,1607,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1621,b,1608,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1621,b,1609,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1621,b,1610,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1621,b,1611,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1621,b,1612,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1621,b,1613,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1621,b,1614,a)].
% 9.32/9.53  Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1621,b,1615,a)].
% 9.32/9.54  1622 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom).  [assumption].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1622,b,1596,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1622,b,1597,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1622,b,1598,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1622,b,1599,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1622,b,1600,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1622,b,1601,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1622,b,1602,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1622,b,1603,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1622,b,1604,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1622,b,1605,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1622,b,1606,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1622,b,1607,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1622,b,1608,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1622,b,1609,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1622,b,1610,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1622,b,1611,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1622,b,1612,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1622,b,1613,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1622,b,1614,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1622,b,1615,a)].
% 9.32/9.54  1623 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom).  [assumption].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1596,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1623,b,1597,a)].
% 9.32/9.54  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1623,b,1598,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1599,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1623,b,1600,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1623,b,1601,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1602,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1623,b,1603,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1623,b,1604,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1623,b,1605,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1623,b,1606,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1623,b,1607,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1623,b,1608,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1623,b,1609,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1623,b,1610,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1623,b,1611,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1623,b,1612,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1623,b,1613,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1623,b,1614,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1623,b,1615,a)].
% 9.32/9.55  1624 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom).  [assumption].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1596,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1624,b,1597,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1624,b,1598,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1599,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1624,b,1600,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1624,b,1601,a)].
% 9.32/9.55  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1602,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1624,b,1603,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1624,b,1604,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1624,b,1605,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1624,b,1606,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1624,b,1607,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1624,b,1608,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1624,b,1609,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1624,b,1610,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1624,b,1611,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1624,b,1612,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1624,b,1613,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1624,b,1614,a)].
% 9.32/9.56  Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1624,b,1615,a)].
% 9.32/9.56  1625 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom).  [assumption].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1596,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1625,b,1597,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1625,b,1598,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1599,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1625,b,1600,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1625,b,1601,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1602,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1625,b,1603,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1625,b,1604,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1625,b,1605,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1625,b,1606,a)].
% 9.32/9.56  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1625,b,1607,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1625,b,1608,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1625,b,1609,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1625,b,1610,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1625,b,1611,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1625,b,1612,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1625,b,1613,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1625,b,1614,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1625,b,1615,a)].
% 9.41/9.57  1626 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom).  [assumption].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1596,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1626,b,1597,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1626,b,1598,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1599,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1626,b,1600,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1626,b,1601,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1602,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1626,b,1603,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1626,b,1604,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1626,b,1605,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1626,b,1606,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1626,b,1607,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1626,b,1608,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1626,b,1609,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1626,b,1610,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1626,b,1611,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1626,b,1612,a)].
% 9.41/9.57  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1626,b,1613,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1626,b,1614,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1626,b,1615,a)].
% 9.41/9.58  1627 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) # label(axiom).  [assumption].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1596,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1627,b,1597,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1627,b,1598,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1599,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1627,b,1600,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1627,b,1601,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1602,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1627,b,1603,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1627,b,1604,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1627,b,1605,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1627,b,1606,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1627,b,1607,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1627,b,1608,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1627,b,1609,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1627,b,1610,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1627,b,1611,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1627,b,1612,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1627,b,1613,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1627,b,1614,a)].
% 9.41/9.58  Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1627,b,1615,a)].
% 9.41/9.58  1628 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom).  [assumption].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1628,b,1596,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1628,b,1597,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1628,b,1598,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1628,b,1599,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1628,b,1600,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1628,b,1601,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1628,b,1602,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1628,b,1603,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1628,b,1604,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1628,b,1605,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1628,b,1606,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1628,b,1607,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1628,b,1608,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1628,b,1609,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1628,b,1610,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1628,b,1611,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1628,b,1612,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1628,b,1613,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1628,b,1614,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1628,b,1615,a)].
% 9.41/9.59  1629 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom).  [assumption].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1629,b,1596,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1629,b,1597,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1629,b,1598,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1629,b,1599,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1629,b,1600,a)].
% 9.41/9.59  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1629,b,1601,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1629,b,1602,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1629,b,1603,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1629,b,1604,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1629,b,1605,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1629,b,1606,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1629,b,1607,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1629,b,1608,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1629,b,1609,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1629,b,1610,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1629,b,1611,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1629,b,1612,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1629,b,1613,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1629,b,1614,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1629,b,1615,a)].
% 9.46/9.61  1630 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom).  [assumption].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1596,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1630,b,1597,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1630,b,1598,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1599,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1630,b,1600,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1630,b,1601,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1602,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1630,b,1603,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1630,b,1604,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1630,b,1605,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1630,b,1606,a)].
% 9.46/9.61  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1630,b,1607,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1630,b,1608,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1630,b,1609,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1630,b,1610,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1630,b,1611,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1630,b,1612,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1630,b,1613,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1630,b,1614,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1630,b,1615,a)].
% 9.46/9.62  1631 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) # label(axiom).  [assumption].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1596,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1631,b,1597,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1631,b,1598,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1599,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1631,b,1600,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1631,b,1601,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1602,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1631,b,1603,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1631,b,1604,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1631,b,1605,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1631,b,1606,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1631,b,1607,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1631,b,1608,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1631,b,1609,a)].
% 9.46/9.62  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1631,b,1610,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1631,b,1611,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1631,b,1612,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1631,b,1613,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1631,b,1614,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1631,b,1615,a)].
% 9.46/9.63  1632 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom).  [assumption].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1596,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1632,b,1597,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1632,b,1598,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1599,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1632,b,1600,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1632,b,1601,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1602,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1632,b,1603,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1632,b,1604,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1632,b,1605,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1632,b,1606,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1632,b,1607,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1632,b,1608,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1632,b,1609,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1632,b,1610,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1632,b,1611,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1632,b,1612,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1632,b,1613,a)].
% 9.46/9.63  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1632,b,1614,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1632,b,1615,a)].
% 9.50/9.64  1633 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom).  [assumption].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1633,b,1596,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1633,b,1597,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1633,b,1598,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1633,b,1599,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1633,b,1600,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1633,b,1601,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1633,b,1602,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1633,b,1603,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1633,b,1604,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1633,b,1605,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1633,b,1606,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1633,b,1607,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1633,b,1608,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1633,b,1609,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1633,b,1610,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1633,b,1611,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1633,b,1612,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1633,b,1613,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1633,b,1614,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1633,b,1615,a)].
% 9.50/9.64  1634 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom).  [assumption].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1596,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1634,b,1597,a)].
% 9.50/9.64  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1634,b,1598,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1599,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1634,b,1600,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1634,b,1601,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1602,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1634,b,1603,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1634,b,1604,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1634,b,1605,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1634,b,1606,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1634,b,1607,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1634,b,1608,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1634,b,1609,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1634,b,1610,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1634,b,1611,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1634,b,1612,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1634,b,1613,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1634,b,1614,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1634,b,1615,a)].
% 9.50/9.65  1635 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom).  [assumption].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1596,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1635,b,1597,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1635,b,1598,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1599,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1635,b,1600,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1635,b,1601,a)].
% 9.50/9.65  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1602,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1635,b,1603,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1635,b,1604,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1635,b,1605,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1635,b,1606,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1635,b,1607,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1635,b,1608,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1635,b,1609,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1635,b,1610,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1635,b,1611,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1635,b,1612,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1635,b,1613,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1635,b,1614,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1635,b,1615,a)].
% 9.51/9.66  1636 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom).  [assumption].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1596,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1636,b,1597,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1636,b,1598,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1599,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1636,b,1600,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1636,b,1601,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1602,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1636,b,1603,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1636,b,1604,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1636,b,1605,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1636,b,1606,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1636,b,1607,a)].
% 9.51/9.66  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1636,b,1608,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1636,b,1609,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1636,b,1610,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1636,b,1611,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1636,b,1612,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1636,b,1613,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1636,b,1614,a)].
% 9.51/9.67  Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1636,b,1615,a)].
% 9.51/9.67  1637 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom).  [assumption].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1596,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1637,b,1597,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1637,b,1598,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1599,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1637,b,1600,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1637,b,1601,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1602,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1637,b,1603,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1637,b,1604,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1637,b,1605,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1637,b,1606,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1637,b,1607,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1637,b,1608,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1637,b,1609,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1637,b,1610,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1637,b,1611,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1637,b,1612,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1637,b,1613,a)].
% 9.51/9.67  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1637,b,1614,a)].
% 10.56/10.75  Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1637,b,1615,a)].
% 10.56/10.75  1638 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(869,a,805,a)].
% 10.56/10.75  1639 class_Orderings_Oord(tc_nat).  [resolve(869,a,864,a)].
% 10.56/10.75  1640 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(869,a,865,b)].
% 10.56/10.75  1641 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(877,b,869,a)].
% 10.56/10.75  1642 -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1050,b,1048,a)].
% 10.56/10.75  1643 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A).  [resolve(1056,b,1048,a)].
% 10.56/10.75  1644 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1138,a,1117,b)].
% 10.56/10.75  1645 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1138,a,1118,b)].
% 10.56/10.75  1646 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1434,a,1417,a)].
% 10.56/10.75  1647 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1435,a,1417,a)].
% 10.56/10.75  1648 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1436,a,1417,a)].
% 10.56/10.75  1649 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1455,a,1448,b)].
% 10.56/10.75  1650 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1455,a,1449,b)].
% 10.56/10.75  1651 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1455,a,1451,b)].
% 10.56/10.75  1652 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A).  [resolve(1463,b,1455,a)].
% 10.56/10.75  1653 class_Orderings_Oord(tc_nat).  [resolve(1469,a,1455,a)].
% 10.56/10.75  1654 class_Orderings_Oord(tc_IntDef_Oint).  [resolve(1472,a,1455,a)].
% 10.56/10.75  1655 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A).  [resolve(1473,b,1455,a)].
% 10.56/10.75  1656 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A).  [resolve(1474,b,1455,a)].
% 10.56/10.75  1657 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1536,b,1510,b)].
% 10.56/10.75  1658 class_Orderings_Oord(tc_set(A)).  [resolve(1562,a,1554,a)].
% 10.56/10.75  1659 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1562,a,1560,b)].
% 10.56/10.75  1660 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1562,a,1561,b)].
% 10.56/10.75  1661 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A).  [resolve(1577,a,1562,a)].
% 10.56/10.75  1662 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A).  [resolve(1578,b,1562,a)].
% 10.56/10.75  1663 -class_LOrder_Olorder(A) | class_Orderings_Oord(A).  [resolve(1579,b,1562,a)].
% 10.56/10.75  1664 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1050,b,1046,a)].
% 10.56/10.75  1665 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom).  [assumption].
% 10.56/10.75  1666 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom).  [assumption].
% 10.56/10.75  1667 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom).  [assumption].
% 10.56/10.75  1668 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom).  [assumption].
% 10.56/10.75  1669 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom).  [assumption].
% 10.56/10.75  1670 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom).  [assumption].
% 10.56/10.75  1671 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) # label(axiom).  [assumption].
% 10.56/10.75  1672 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom).  [assumption].
% 10.56/10.75  1673 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom).  [assumption].
% 10.71/10.87  1674 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom).  [assumption].
% 10.71/10.87  1675 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom).  [assumption].
% 10.71/10.87  1676 class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(866,a,805,a)].
% 10.71/10.87  1677 class_LOrder_Olorder(tc_nat).  [resolve(866,a,864,a)].
% 10.71/10.87  1678 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(866,a,865,b)].
% 10.71/10.87  1679 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A).  [resolve(877,b,866,a)].
% 10.71/10.87  1680 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1071,b,1069,a)].
% 10.71/10.87  1681 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1129,a,1117,b)].
% 10.71/10.87  1682 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1129,a,1118,b)].
% 10.71/10.87  1683 class_LOrder_Olorder(tc_IntDef_Oint).  [resolve(1434,a,1415,a)].
% 10.71/10.87  1684 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A).  [resolve(1435,a,1415,a)].
% 10.71/10.87  1685 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A).  [resolve(1436,a,1415,a)].
% 10.71/10.87  1686 -class_LOrder_Olorder(A) | -c_less(B,B,A).  [resolve(1555,b,1542,a)].
% 10.71/10.87  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1686,a,1665,a)].
% 10.71/10.87  Derived: -c_less(A,A,tc_nat).  [resolve(1686,a,1666,a)].
% 10.71/10.87  1687 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1543,a)].
% 10.71/10.87  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1687,a,1665,a)].
% 10.71/10.87  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1687,a,1666,a)].
% 10.71/10.87  1688 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1544,a)].
% 10.71/10.87  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1688,a,1665,a)].
% 10.71/10.87  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1688,a,1666,a)].
% 10.71/10.87  1689 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1555,b,1545,a)].
% 10.71/10.87  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1689,a,1665,a)].
% 10.71/10.87  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1689,a,1666,a)].
% 10.71/10.87  1690 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1555,b,1546,a)].
% 10.71/10.87  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1690,a,1665,a)].
% 10.71/10.87  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(1690,a,1666,a)].
% 10.71/10.87  1691 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1555,b,1547,a)].
% 10.71/10.87  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1691,a,1665,a)].
% 10.71/10.87  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(1691,a,1666,a)].
% 10.71/10.87  1692 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1555,b,1548,a)].
% 10.71/10.87  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1692,a,1665,a)].
% 10.71/10.87  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(1692,a,1666,a)].
% 10.71/10.92  1693 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1555,b,1549,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1693,a,1665,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(1693,a,1666,a)].
% 10.71/10.92  1694 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1555,b,1550,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1694,a,1665,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1694,a,1666,a)].
% 10.71/10.92  1695 -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1555,b,1551,a)].
% 10.71/10.92  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1695,a,1665,a)].
% 10.71/10.92  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(1695,a,1666,a)].
% 10.71/10.92  1696 -class_LOrder_Olorder(A) | c_lessequals(B,B,A).  [resolve(1555,b,1552,a)].
% 10.71/10.92  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1696,a,1665,a)].
% 10.71/10.92  Derived: c_lessequals(A,A,tc_nat).  [resolve(1696,a,1666,a)].
% 10.71/10.92  1697 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1596,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1697,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1697,a,1666,a)].
% 10.71/10.92  1698 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1618,b,1597,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1698,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1698,a,1666,a)].
% 10.71/10.92  1699 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1618,b,1598,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1699,a,1665,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(1699,a,1666,a)].
% 10.71/10.92  1700 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1599,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1700,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1700,a,1666,a)].
% 10.71/10.92  1701 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1618,b,1600,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1701,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1701,a,1666,a)].
% 10.71/10.92  1702 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1618,b,1601,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1702,a,1665,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(1702,a,1666,a)].
% 10.71/10.92  1703 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1618,b,1602,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1703,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1703,a,1666,a)].
% 10.71/10.92  1704 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1618,b,1603,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1704,a,1665,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1704,a,1666,a)].
% 10.71/10.92  1705 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1618,b,1604,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1705,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1705,a,1666,a)].
% 10.71/10.92  1706 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1618,b,1605,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1706,a,1665,a)].
% 10.71/10.92  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1706,a,1666,a)].
% 10.71/10.92  1707 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1618,b,1606,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1707,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1707,a,1666,a)].
% 10.71/10.92  1708 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1618,b,1607,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1708,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1708,a,1666,a)].
% 10.71/10.92  1709 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1618,b,1608,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1709,a,1665,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(1709,a,1666,a)].
% 10.71/10.92  1710 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1618,b,1609,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1710,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1710,a,1666,a)].
% 10.71/10.92  1711 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1618,b,1610,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1711,a,1665,a)].
% 10.71/10.92  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1711,a,1666,a)].
% 10.71/10.92  1712 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1618,b,1611,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1712,a,1665,a)].
% 10.71/10.92  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(1712,a,1666,a)].
% 10.98/11.11  1713 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1618,b,1612,a)].
% 10.98/11.11  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1713,a,1665,a)].
% 10.98/11.11  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1713,a,1666,a)].
% 10.98/11.11  1714 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1618,b,1613,a)].
% 10.98/11.11  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1714,a,1665,a)].
% 10.98/11.11  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1714,a,1666,a)].
% 10.98/11.11  1715 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1618,b,1614,a)].
% 10.98/11.11  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(1715,a,1665,a)].
% 10.98/11.11  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1715,a,1666,a)].
% 10.98/11.11  1716 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1618,b,1615,a)].
% 10.98/11.11  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1716,a,1665,a)].
% 10.98/11.11  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1716,a,1666,a)].
% 10.98/11.11  1717 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom).  [assumption].
% 10.98/11.11  1718 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom).  [assumption].
% 10.98/11.11  1719 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom).  [assumption].
% 10.98/11.11  1720 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_7) # label(axiom).  [assumption].
% 10.98/11.11  1721 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_7) # label(axiom).  [assumption].
% 10.98/11.11  1722 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) # label(axiom).  [assumption].
% 10.98/11.11  1723 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_9) # label(axiom).  [assumption].
% 10.98/11.11  1724 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) # label(axiom).  [assumption].
% 10.98/11.11  1725 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) # label(axiom).  [assumption].
% 10.98/11.11  1726 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_9) # label(axiom).  [assumption].
% 10.98/11.11  1727 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) # label(axiom).  [assumption].
% 10.98/11.11  1728 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_57) # label(axiom).  [assumption].
% 10.98/11.11  1729 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_43) # label(axiom).  [assumption].
% 10.98/11.11  1730 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_16) # label(axiom).  [assumption].
% 10.98/11.11  1731 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) # label(axiom).  [assumption].
% 11.16/11.35  1732 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_7) # label(axiom).  [assumption].
% 11.16/11.35  1733 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_22) # label(axiom).  [assumption].
% 11.16/11.35  1734 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_12) # label(axiom).  [assumption].
% 11.16/11.35  1735 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_16) # label(axiom).  [assumption].
% 11.16/11.35  1736 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_9) # label(axiom).  [assumption].
% 11.16/11.35  1737 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1136,a,1091,a)].
% 11.16/11.35  1738 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).  [resolve(1136,a,1116,a)].
% 11.16/11.35  1739 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1136,a,1117,b)].
% 11.16/11.35  1740 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1136,a,1118,b)].
% 11.16/11.35  1741 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1424,a)].
% 11.16/11.35  1742 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1435,a,1424,a)].
% 11.16/11.35  1743 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1436,a,1424,a)].
% 11.16/11.35  1744 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1453,a,1448,b)].
% 11.16/11.35  1745 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1453,a,1449,b)].
% 11.16/11.35  1746 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1453,a,1450,b)].
% 11.16/11.35  1747 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1453,a,1451,b)].
% 11.16/11.35  1748 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A).  [resolve(1463,b,1453,a)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1748,b,1717,a)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(1748,b,1724,a)].
% 11.16/11.35  1749 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1534,b,1475,a)].
% 11.16/11.35  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(1749,a,1717,a)].
% 11.16/11.35  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(1749,a,1724,a)].
% 11.16/11.35  1750 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1534,b,1510,b)].
% 11.16/11.35  1751 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1534,b,1511,b)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1751,a,1717,a)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A).  [resolve(1751,a,1724,a)].
% 11.16/11.35  1752 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1534,b,1512,b)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1752,a,1717,a)].
% 11.16/11.35  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A).  [resolve(1752,a,1724,a)].
% 11.16/11.35  1753 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1560,b,1542,a)].
% 11.16/11.35  Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1753,a,1720,b)].
% 11.16/11.35  Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1753,a,1721,b)].
% 11.16/11.35  Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1753,a,1722,b)].
% 11.16/11.35  Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1753,a,1723,b)].
% 11.16/11.35  1754 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1560,b,1543,a)].
% 11.16/11.35  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1754,a,1720,b)].
% 11.16/11.35  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1754,a,1721,b)].
% 11.16/11.35  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1754,a,1722,b)].
% 11.16/11.35  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1754,a,1723,b)].
% 11.16/11.35  1755 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1560,b,1544,a)].
% 11.16/11.35  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1755,a,1720,b)].
% 11.16/11.35  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1755,a,1721,b)].
% 11.16/11.35  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1755,a,1722,b)].
% 11.16/11.35  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1755,a,1723,b)].
% 11.16/11.35  1756 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1560,b,1545,a)].
% 11.16/11.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1756,a,1720,b)].
% 11.16/11.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1756,a,1721,b)].
% 11.16/11.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1756,a,1722,b)].
% 11.16/11.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1756,a,1723,b)].
% 11.16/11.35  1757 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1560,b,1546,a)].
% 11.16/11.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1757,a,1720,b)].
% 11.16/11.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1757,a,1721,b)].
% 11.16/11.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1757,a,1722,b)].
% 11.16/11.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1757,a,1723,b)].
% 11.16/11.35  1758 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1560,b,1547,a)].
% 11.16/11.35  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1758,a,1720,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1758,a,1721,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1758,a,1722,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1758,a,1723,b)].
% 11.23/11.36  1759 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1560,b,1548,a)].
% 11.23/11.36  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1759,a,1720,b)].
% 11.23/11.36  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1759,a,1721,b)].
% 11.23/11.36  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1759,a,1722,b)].
% 11.23/11.36  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1759,a,1723,b)].
% 11.23/11.36  1760 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1560,b,1549,a)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1760,a,1720,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1760,a,1721,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1760,a,1722,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1760,a,1723,b)].
% 11.23/11.36  1761 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1560,b,1550,a)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1761,a,1720,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1761,a,1721,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1761,a,1722,b)].
% 11.23/11.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1761,a,1723,b)].
% 11.23/11.36  1762 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1560,b,1551,a)].
% 11.23/11.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1762,a,1720,b)].
% 11.23/11.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1762,a,1721,b)].
% 11.23/11.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1762,a,1722,b)].
% 11.25/11.41  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1762,a,1723,b)].
% 11.25/11.41  1763 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1560,b,1552,a)].
% 11.25/11.41  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1763,a,1720,b)].
% 11.25/11.41  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1763,a,1721,b)].
% 11.25/11.41  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1763,a,1722,b)].
% 11.25/11.41  Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B).  [resolve(1763,a,1723,b)].
% 11.25/11.41  1764 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1596,a)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1764,a,1720,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1764,a,1721,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1764,a,1722,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1764,a,1723,b)].
% 11.25/11.41  1765 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1623,b,1597,a)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1765,a,1720,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1765,a,1721,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1765,a,1722,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1765,a,1723,b)].
% 11.25/11.41  1766 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1623,b,1598,a)].
% 11.25/11.41  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1766,a,1720,b)].
% 11.25/11.41  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1766,a,1721,b)].
% 11.25/11.41  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1766,a,1722,b)].
% 11.25/11.41  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1766,a,1723,b)].
% 11.25/11.41  1767 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1599,a)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1767,a,1720,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1767,a,1721,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1767,a,1722,b)].
% 11.25/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1767,a,1723,b)].
% 11.29/11.41  1768 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1623,b,1600,a)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1768,a,1720,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1768,a,1721,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1768,a,1722,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1768,a,1723,b)].
% 11.29/11.41  1769 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1623,b,1601,a)].
% 11.29/11.41  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1769,a,1720,b)].
% 11.29/11.41  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1769,a,1721,b)].
% 11.29/11.41  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1769,a,1722,b)].
% 11.29/11.41  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1769,a,1723,b)].
% 11.29/11.41  1770 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1623,b,1602,a)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1770,a,1720,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1770,a,1721,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1770,a,1722,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1770,a,1723,b)].
% 11.29/11.41  1771 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1623,b,1603,a)].
% 11.29/11.41  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1771,a,1720,b)].
% 11.29/11.41  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1771,a,1721,b)].
% 11.29/11.41  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1771,a,1722,b)].
% 11.29/11.41  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1771,a,1723,b)].
% 11.29/11.41  1772 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1623,b,1604,a)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1772,a,1720,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1772,a,1721,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1772,a,1722,b)].
% 11.29/11.41  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1772,a,1723,b)].
% 11.29/11.41  1773 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1623,b,1605,a)].
% 11.29/11.42  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1773,a,1720,b)].
% 11.29/11.42  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1773,a,1721,b)].
% 11.29/11.42  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1773,a,1722,b)].
% 11.29/11.42  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1773,a,1723,b)].
% 11.29/11.42  1774 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1623,b,1606,a)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1774,a,1720,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1774,a,1721,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1774,a,1722,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1774,a,1723,b)].
% 11.29/11.42  1775 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1623,b,1607,a)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1775,a,1720,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1775,a,1721,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1775,a,1722,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1775,a,1723,b)].
% 11.29/11.42  1776 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1623,b,1608,a)].
% 11.29/11.42  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1776,a,1720,b)].
% 11.29/11.42  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1776,a,1721,b)].
% 11.29/11.42  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1776,a,1722,b)].
% 11.29/11.42  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1776,a,1723,b)].
% 11.29/11.42  1777 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1623,b,1609,a)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1777,a,1720,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1777,a,1721,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1777,a,1722,b)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1777,a,1723,b)].
% 11.29/11.42  1778 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1623,b,1610,a)].
% 11.29/11.42  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1778,a,1720,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1778,a,1721,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1778,a,1722,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D).  [resolve(1778,a,1723,b)].
% 11.29/11.43  1779 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1623,b,1611,a)].
% 11.29/11.43  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1779,a,1720,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1779,a,1721,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1779,a,1722,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1779,a,1723,b)].
% 11.29/11.43  1780 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1623,b,1612,a)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1780,a,1720,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1780,a,1721,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1780,a,1722,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1780,a,1723,b)].
% 11.29/11.43  1781 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1623,b,1613,a)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1781,a,1720,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1781,a,1721,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1781,a,1722,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1781,a,1723,b)].
% 11.29/11.43  1782 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1623,b,1614,a)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1782,a,1720,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1782,a,1721,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1782,a,1722,b)].
% 11.29/11.43  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1782,a,1723,b)].
% 11.29/11.43  1783 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1623,b,1615,a)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1783,a,1720,b)].
% 11.29/11.43  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1783,a,1721,b)].
% 11.55/11.68  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1783,a,1722,b)].
% 11.55/11.68  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C).  [resolve(1783,a,1723,b)].
% 11.55/11.68  1784 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) # label(axiom).  [assumption].
% 11.55/11.68  1785 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom).  [assumption].
% 11.55/11.68  1786 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom).  [assumption].
% 11.55/11.68  1787 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_6) # label(axiom).  [assumption].
% 11.55/11.68  1788 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_6) # label(axiom).  [assumption].
% 11.55/11.68  1789 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) # label(axiom).  [assumption].
% 11.55/11.68  1790 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_13) # label(axiom).  [assumption].
% 11.55/11.68  1791 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # label(axiom).  [assumption].
% 11.55/11.68  1792 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_6) # label(axiom).  [assumption].
% 11.55/11.68  1793 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) # label(axiom).  [assumption].
% 11.55/11.68  1794 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_56) # label(axiom).  [assumption].
% 11.55/11.68  1795 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_38) # label(axiom).  [assumption].
% 11.55/11.68  1796 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_15) # label(axiom).  [assumption].
% 11.55/11.68  1797 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_21) # label(axiom).  [assumption].
% 11.55/11.68  1798 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(18,b,1,a)].
% 11.55/11.68  1799 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(18,b,3,a)].
% 11.55/11.68  1800 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(18,b,9,a)].
% 11.55/11.68  1801 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(18,b,10,a)].
% 11.55/11.68  1802 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(749,b,708,a)].
% 11.55/11.68  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1802,a,1793,b)].
% 11.55/11.68  1803 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A).  [resolve(749,b,715,a)].
% 11.55/11.68  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1803,a,1793,b)].
% 11.70/11.88  1804 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1131,a,1091,a)].
% 11.70/11.88  1805 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1131,a,1116,a)].
% 11.70/11.88  1806 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1131,a,1117,b)].
% 11.70/11.88  1807 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1131,a,1118,b)].
% 11.70/11.88  1808 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1434,a,1423,a)].
% 11.70/11.88  1809 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1435,a,1423,a)].
% 11.70/11.88  1810 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A).  [resolve(1436,a,1423,a)].
% 11.70/11.88  1811 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1452,a,1448,b)].
% 11.70/11.88  1812 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1452,a,1449,b)].
% 11.70/11.88  1813 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1452,a,1450,b)].
% 11.70/11.88  1814 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1452,a,1451,b)].
% 11.70/11.88  1815 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1533,b,1475,a)].
% 11.70/11.88  1816 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1533,b,1510,b)].
% 11.70/11.88  1817 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1533,b,1511,b)].
% 11.70/11.88  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(1817,a,1798,a)].
% 11.70/11.88  Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(1817,a,1799,a)].
% 11.70/11.88  1818 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1533,b,1512,b)].
% 11.70/11.88  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(1818,a,1798,a)].
% 11.70/11.88  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(1818,a,1799,a)].
% 11.70/11.88  1819 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1561,b,1542,a)].
% 11.70/11.88  1820 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1561,b,1543,a)].
% 11.70/11.88  1821 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1561,b,1544,a)].
% 11.70/11.88  1822 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1561,b,1545,a)].
% 11.70/11.88  1823 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1561,b,1546,a)].
% 11.70/11.88  1824 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1561,b,1547,a)].
% 11.70/11.88  1825 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1561,b,1548,a)].
% 11.70/11.88  1826 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1561,b,1549,a)].
% 11.70/11.88  1827 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1561,b,1550,a)].
% 11.70/11.88  1828 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1561,b,1551,a)].
% 11.99/12.13  1829 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1561,b,1552,a)].
% 11.99/12.13  1830 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1596,a)].
% 11.99/12.13  1831 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1624,b,1597,a)].
% 11.99/12.13  1832 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1624,b,1598,a)].
% 11.99/12.13  1833 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1599,a)].
% 11.99/12.13  1834 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1624,b,1600,a)].
% 11.99/12.13  1835 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1624,b,1601,a)].
% 11.99/12.13  1836 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1624,b,1602,a)].
% 11.99/12.13  1837 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1624,b,1603,a)].
% 11.99/12.13  1838 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1624,b,1604,a)].
% 11.99/12.13  1839 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1624,b,1605,a)].
% 11.99/12.13  1840 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1624,b,1606,a)].
% 11.99/12.13  1841 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1624,b,1607,a)].
% 11.99/12.13  1842 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1624,b,1608,a)].
% 11.99/12.13  1843 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1624,b,1609,a)].
% 11.99/12.13  1844 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1624,b,1610,a)].
% 11.99/12.13  1845 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1624,b,1611,a)].
% 11.99/12.13  1846 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1624,b,1612,a)].
% 11.99/12.13  1847 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1624,b,1613,a)].
% 11.99/12.13  1848 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1624,b,1614,a)].
% 11.99/12.13  1849 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1624,b,1615,a)].
% 11.99/12.13  1850 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) # label(axiom).  [assumption].
% 11.99/12.13  1851 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom).  [assumption].
% 11.99/12.13  1852 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom).  [assumption].
% 11.99/12.13  1853 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) # label(axiom).  [assumption].
% 12.07/12.20  1854 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) # label(axiom).  [assumption].
% 12.07/12.20  1855 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_40) # label(axiom).  [assumption].
% 12.07/12.20  1856 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_32) # label(axiom).  [assumption].
% 12.07/12.20  1857 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_9) # label(axiom).  [assumption].
% 12.07/12.20  1858 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(15,b,1,a)].
% 12.07/12.20  1859 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(15,b,3,a)].
% 12.07/12.20  1860 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(81,b,53,b)].
% 12.07/12.20  1861 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(82,b,53,b)].
% 12.07/12.20  1862 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(865,b,806,a)].
% 12.07/12.20  1863 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(865,b,807,a)].
% 12.07/12.20  1864 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(865,b,808,a)].
% 12.07/12.20  1865 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(865,b,809,a)].
% 12.07/12.20  1866 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,810,a)].
% 12.07/12.20  1867 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,811,a)].
% 12.07/12.20  1868 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(865,b,812,a)].
% 12.07/12.20  1869 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,813,a)].
% 12.07/12.20  1870 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(865,b,814,a)].
% 12.07/12.20  1871 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(865,b,815,a)].
% 12.07/12.20  1872 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(865,b,816,a)].
% 12.07/12.20  1873 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,817,a)].
% 12.07/12.20  1874 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,818,a)].
% 12.07/12.21  1875 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(865,b,819,a)].
% 12.07/12.21  1876 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,820,a)].
% 12.07/12.21  1877 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(865,b,821,a)].
% 12.07/12.21  1878 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(865,b,822,a)].
% 12.07/12.21  1879 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(865,b,823,a)].
% 12.07/12.21  1880 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(865,b,824,a)].
% 12.07/12.21  1881 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(865,b,825,a)].
% 12.07/12.21  1882 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(865,b,826,a)].
% 12.07/12.21  1883 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(865,b,827,a)].
% 12.07/12.21  1884 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(865,b,828,a)].
% 12.07/12.21  1885 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(865,b,829,b)].
% 12.07/12.21  1886 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(865,b,830,b)].
% 12.07/12.21  1887 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(865,b,831,a)].
% 12.07/12.21  1888 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(865,b,832,a)].
% 12.07/12.21  1889 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(865,b,833,a)].
% 12.07/12.21  1890 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(865,b,834,a)].
% 12.07/12.21  1891 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(865,b,835,a)].
% 12.07/12.21  1892 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(865,b,836,a)].
% 12.07/12.21  1893 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(865,b,837,a)].
% 12.07/12.21  1894 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(865,b,838,a)].
% 12.07/12.21  1895 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(865,b,839,a)].
% 12.07/12.22  1896 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(865,b,840,a)].
% 12.07/12.22  1897 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(865,b,841,a)].
% 12.07/12.22  1898 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(865,b,842,a)].
% 12.07/12.22  1899 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(865,b,843,a)].
% 12.07/12.22  1900 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(865,b,844,a)].
% 12.07/12.22  1901 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(865,b,845,a)].
% 12.07/12.22  1902 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(865,b,846,a)].
% 12.07/12.22  1903 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(865,b,847,a)].
% 12.07/12.22  1904 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(865,b,848,a)].
% 12.07/12.22  1905 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(865,b,849,a)].
% 12.07/12.22  1906 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(865,b,850,a)].
% 12.07/12.22  1907 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(865,b,851,a)].
% 12.07/12.22  1908 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(865,b,852,a)].
% 12.07/12.22  1909 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(865,b,853,a)].
% 12.07/12.22  1910 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(865,b,854,a)].
% 12.07/12.22  1911 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(865,b,855,a)].
% 12.07/12.22  1912 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(865,b,856,a)].
% 12.07/12.22  1913 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(865,b,857,a)].
% 12.07/12.22  1914 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(865,b,858,a)].
% 12.07/12.22  1915 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(865,b,859,a)].
% 12.07/12.22  1916 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(865,b,860,a)].
% 12.07/12.22  1917 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(865,b,861,a)].
% 12.07/12.22  1918 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(865,b,862,a)].
% 12.20/12.36  1919 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(865,b,863,a)].
% 12.20/12.36  1920 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1055,b,1046,a)].
% 12.20/12.36  1921 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1078,b,1069,a)].
% 12.20/12.36  1922 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint).  [resolve(1128,a,1091,a)].
% 12.20/12.36  1923 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat).  [resolve(1128,a,1116,a)].
% 12.20/12.36  1924 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1128,a,1117,b)].
% 12.20/12.36  1925 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1128,a,1118,b)].
% 12.20/12.36  1926 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1450,b,1438,a)].
% 12.20/12.36  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(1926,a,1852,a)].
% 12.20/12.36  1927 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1450,b,1439,a)].
% 12.20/12.36  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(1927,a,1852,a)].
% 12.20/12.36  1928 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1450,b,1440,a)].
% 12.20/12.36  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1928,a,1852,a)].
% 12.20/12.36  1929 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1450,b,1441,a)].
% 12.20/12.36  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(1929,a,1852,a)].
% 12.20/12.36  1930 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1450,b,1442,a)].
% 12.20/12.36  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat).  [resolve(1930,a,1852,a)].
% 12.20/12.36  1931 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1450,b,1443,a)].
% 12.20/12.36  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(1931,a,1852,a)].
% 12.20/12.36  1932 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1450,b,1444,a)].
% 12.20/12.36  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1932,a,1852,a)].
% 12.20/12.36  1933 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1450,b,1445,a)].
% 12.20/12.36  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(1933,a,1852,a)].
% 12.20/12.36  1934 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1464,a,1450,b)].
% 12.20/12.36  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1934,c,1854,b)].
% 12.20/12.36  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1934,c,1857,b)].
% 12.20/12.36  1935 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1465,a,1450,b)].
% 12.20/12.36  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1935,c,1854,b)].
% 12.20/12.36  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1935,c,1857,b)].
% 12.20/12.36  1936 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1466,b,1450,b)].
% 12.20/12.42  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(1936,b,1852,a)].
% 12.20/12.42  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1936,b,1857,b)].
% 12.20/12.42  1937 class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A).  [resolve(1467,b,1450,b)].
% 12.20/12.42  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1937,b,1857,b)].
% 12.20/12.42  1938 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A).  [resolve(1558,b,1542,a)].
% 12.20/12.42  1939 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1558,b,1543,a)].
% 12.20/12.42  1940 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1558,b,1544,a)].
% 12.20/12.42  1941 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1558,b,1545,a)].
% 12.20/12.42  1942 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1558,b,1546,a)].
% 12.20/12.42  1943 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1558,b,1547,a)].
% 12.20/12.42  1944 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1558,b,1548,a)].
% 12.20/12.42  1945 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1558,b,1549,a)].
% 12.20/12.42  1946 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1558,b,1550,a)].
% 12.20/12.42  1947 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1558,b,1551,a)].
% 12.20/12.42  1948 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A).  [resolve(1558,b,1552,a)].
% 12.20/12.42  1949 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1596,a)].
% 12.20/12.42  1950 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1621,b,1597,a)].
% 12.20/12.42  1951 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1621,b,1598,a)].
% 12.20/12.42  1952 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1599,a)].
% 12.20/12.42  1953 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1621,b,1600,a)].
% 12.20/12.42  1954 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1621,b,1601,a)].
% 12.20/12.42  1955 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1621,b,1602,a)].
% 12.20/12.42  1956 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1621,b,1603,a)].
% 12.20/12.42  1957 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1621,b,1604,a)].
% 12.20/12.42  1958 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1621,b,1605,a)].
% 12.20/12.42  1959 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1621,b,1606,a)].
% 12.31/12.48  1960 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1621,b,1607,a)].
% 12.31/12.48  1961 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1621,b,1608,a)].
% 12.31/12.48  1962 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1621,b,1609,a)].
% 12.31/12.48  1963 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1621,b,1610,a)].
% 12.31/12.48  1964 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1621,b,1611,a)].
% 12.31/12.48  1965 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1621,b,1612,a)].
% 12.31/12.48  1966 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1621,b,1613,a)].
% 12.31/12.48  1967 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1621,b,1614,a)].
% 12.31/12.48  1968 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1621,b,1615,a)].
% 12.31/12.48  1969 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1753,a,1722,b)].
% 12.31/12.48  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(1969,b,1851,a)].
% 12.31/12.48  Derived: -c_less(A,A,tc_nat).  [resolve(1969,b,1852,a)].
% 12.31/12.48  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1969,b,1854,b)].
% 12.31/12.48  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1969,b,1855,b)].
% 12.31/12.48  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1969,b,1856,b)].
% 12.31/12.48  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1969,b,1857,b)].
% 12.31/12.48  1970 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1754,a,1722,b)].
% 12.31/12.48  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1970,c,1851,a)].
% 12.31/12.48  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1970,c,1852,a)].
% 12.31/12.48  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1970,c,1854,b)].
% 12.31/12.48  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1970,c,1855,b)].
% 12.31/12.48  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1970,c,1856,b)].
% 12.31/12.48  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1970,c,1857,b)].
% 12.31/12.48  1971 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1755,a,1722,b)].
% 12.31/12.48  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1971,b,1851,a)].
% 12.31/12.48  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(1971,b,1852,a)].
% 12.31/12.48  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1971,b,1854,b)].
% 12.31/12.48  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1971,b,1855,b)].
% 12.31/12.48  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1971,b,1856,b)].
% 12.31/12.49  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1971,b,1857,b)].
% 12.31/12.49  1972 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1756,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1972,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(1972,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1972,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1972,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1972,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1972,c,1857,b)].
% 12.31/12.49  1973 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1757,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1973,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(1973,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1973,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1973,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1973,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1973,c,1857,b)].
% 12.31/12.49  1974 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1758,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1974,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(1974,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1974,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1974,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1974,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1974,c,1857,b)].
% 12.31/12.49  1975 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1759,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1975,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(1975,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1975,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1975,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1975,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1975,c,1857,b)].
% 12.31/12.49  1976 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1760,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(1976,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(1976,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1976,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1976,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1976,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1976,c,1857,b)].
% 12.31/12.49  1977 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1761,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(1977,c,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(1977,c,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1977,c,1854,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(1977,c,1855,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1977,c,1856,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1977,c,1857,b)].
% 12.31/12.49  1978 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1762,a,1722,b)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(1978,b,1851,a)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(1978,b,1852,a)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1978,b,1854,b)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1978,b,1855,b)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1978,b,1856,b)].
% 12.31/12.49  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1978,b,1857,b)].
% 12.31/12.49  1979 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B).  [resolve(1763,a,1722,b)].
% 12.31/12.49  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(1979,b,1851,a)].
% 12.31/12.49  Derived: c_lessequals(A,A,tc_nat).  [resolve(1979,b,1852,a)].
% 12.31/12.49  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1979,b,1854,b)].
% 12.31/12.49  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(1979,b,1855,b)].
% 12.31/12.49  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(1979,b,1856,b)].
% 12.31/12.49  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1979,b,1857,b)].
% 12.31/12.49  1980 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1764,a,1722,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1980,c,1851,a)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1980,c,1852,a)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1980,c,1854,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1980,c,1855,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1980,c,1856,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1980,c,1857,b)].
% 12.31/12.49  1981 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1765,a,1722,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1981,c,1851,a)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1981,c,1852,a)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1981,c,1854,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1981,c,1855,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1981,c,1856,b)].
% 12.31/12.49  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1981,c,1857,b)].
% 12.31/12.49  1982 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1766,a,1722,b)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1982,d,1851,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(1982,d,1852,a)].
% 12.31/12.49  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1982,d,1854,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1982,d,1855,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1982,d,1856,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1982,d,1857,b)].
% 12.31/12.50  1983 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1767,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1983,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1983,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1983,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1983,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1983,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1983,c,1857,b)].
% 12.31/12.50  1984 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1768,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1984,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1984,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1984,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1984,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1984,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1984,c,1857,b)].
% 12.31/12.50  1985 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1769,a,1722,b)].
% 12.31/12.50  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1985,d,1851,a)].
% 12.31/12.50  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(1985,d,1852,a)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1985,d,1854,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1985,d,1855,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1985,d,1856,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1985,d,1857,b)].
% 12.31/12.50  1986 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1770,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(1986,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1986,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1986,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1986,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1986,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1986,c,1857,b)].
% 12.31/12.50  1987 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1771,a,1722,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1987,c,1851,a)].
% 12.31/12.50  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(1987,c,1852,a)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1987,c,1854,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1987,c,1855,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1987,c,1856,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1987,c,1857,b)].
% 12.31/12.50  1988 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1772,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(1988,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(1988,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1988,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1988,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1988,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1988,c,1857,b)].
% 12.31/12.50  1989 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1773,a,1722,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1989,c,1851,a)].
% 12.31/12.50  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(1989,c,1852,a)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1989,c,1854,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1989,c,1855,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1989,c,1856,b)].
% 12.31/12.50  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1989,c,1857,b)].
% 12.31/12.50  1990 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1774,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1990,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1990,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1990,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1990,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1990,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1990,c,1857,b)].
% 12.31/12.50  1991 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1775,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(1991,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(1991,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1991,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1991,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1991,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1991,c,1857,b)].
% 12.31/12.50  1992 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1776,a,1722,b)].
% 12.31/12.50  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1992,d,1851,a)].
% 12.31/12.50  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(1992,d,1852,a)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1992,d,1854,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1992,d,1855,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1992,d,1856,b)].
% 12.31/12.50  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1992,d,1857,b)].
% 12.31/12.50  1993 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1777,a,1722,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1993,c,1851,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1993,c,1852,a)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1993,c,1854,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1993,c,1855,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1993,c,1856,b)].
% 12.31/12.50  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1993,c,1857,b)].
% 12.31/12.51  1994 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D).  [resolve(1778,a,1722,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(1994,c,1851,a)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(1994,c,1852,a)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1994,c,1854,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(1994,c,1855,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(1994,c,1856,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1994,c,1857,b)].
% 12.31/12.51  1995 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1779,a,1722,b)].
% 12.31/12.51  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1995,d,1851,a)].
% 12.31/12.51  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(1995,d,1852,a)].
% 12.31/12.51  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1995,d,1854,b)].
% 12.31/12.51  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1995,d,1855,b)].
% 12.31/12.51  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1995,d,1856,b)].
% 12.31/12.51  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1995,d,1857,b)].
% 12.31/12.51  1996 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1780,a,1722,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(1996,c,1851,a)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(1996,c,1852,a)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1996,c,1854,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1996,c,1855,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1996,c,1856,b)].
% 12.31/12.51  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1996,c,1857,b)].
% 12.31/12.51  1997 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1781,a,1722,b)].
% 12.31/12.51  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1997,c,1851,a)].
% 12.31/12.51  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(1997,c,1852,a)].
% 12.31/12.51  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1997,c,1854,b)].
% 12.31/12.51  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1997,c,1855,b)].
% 12.31/12.51  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1997,c,1856,b)].
% 12.53/12.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1997,c,1857,b)].
% 12.53/12.66  1998 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1782,a,1722,b)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(1998,c,1851,a)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(1998,c,1852,a)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1998,c,1854,b)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1998,c,1855,b)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1998,c,1856,b)].
% 12.53/12.66  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1998,c,1857,b)].
% 12.53/12.66  1999 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C).  [resolve(1783,a,1722,b)].
% 12.53/12.66  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(1999,c,1851,a)].
% 12.53/12.66  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(1999,c,1852,a)].
% 12.53/12.66  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1999,c,1854,b)].
% 12.53/12.66  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(1999,c,1855,b)].
% 12.53/12.66  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(1999,c,1856,b)].
% 12.53/12.66  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1999,c,1857,b)].
% 12.53/12.66  2000 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom).  [assumption].
% 12.53/12.66  2001 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom).  [assumption].
% 12.53/12.66  2002 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom).  [assumption].
% 12.53/12.66  2003 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_8) # label(axiom).  [assumption].
% 12.53/12.66  2004 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) # label(axiom).  [assumption].
% 12.53/12.66  2005 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_46) # label(axiom).  [assumption].
% 12.53/12.66  2006 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_42) # label(axiom).  [assumption].
% 12.53/12.66  2007 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_23) # label(axiom).  [assumption].
% 12.53/12.66  2008 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) # label(axiom).  [assumption].
% 12.53/12.66  2009 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_0) # label(axiom).  [assumption].
% 12.53/12.66  2010 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_21) # label(axiom).  [assumption].
% 12.57/12.69  2011 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_15) # label(axiom).  [assumption].
% 12.57/12.69  2012 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Opordered__semiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_15) # label(axiom).  [assumption].
% 12.57/12.69  2013 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__semiring_3) # label(axiom).  [assumption].
% 12.57/12.69  2014 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom).  [assumption].
% 12.57/12.69  2015 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom).  [assumption].
% 12.57/12.69  2016 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__semiring_7) # label(axiom).  [assumption].
% 12.57/12.69  2017 -class_Ring__and__Field_Opordered__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__semiring_8) # label(axiom).  [assumption].
% 12.57/12.69  2018 -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(159,b,131,b)].
% 12.57/12.69  2019 -class_Ring__and__Field_Opordered__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(159,b,133,b)].
% 12.57/12.69  2020 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(163,a,159,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2020,b,2011,b)].
% 12.57/12.69  2021 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(164,a,159,b)].
% 12.57/12.69  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2021,b,2011,b)].
% 12.57/12.69  2022 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(165,a,159,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2022,b,2004,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2022,b,2007,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2022,b,2008,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2022,b,2009,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2022,b,2011,b)].
% 12.57/12.69  2023 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(166,a,159,b)].
% 12.57/12.69  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2023,b,2004,b)].
% 12.57/12.69  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2023,b,2007,b)].
% 12.57/12.69  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2023,b,2008,b)].
% 12.57/12.69  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2023,b,2009,b)].
% 12.57/12.69  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2023,b,2011,b)].
% 12.57/12.69  2024 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(236,a,229,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2024,b,2004,b)].
% 12.57/12.69  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2024,b,2007,b)].
% 12.57/12.70  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2024,b,2008,b)].
% 12.57/12.70  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2024,b,2009,b)].
% 12.57/12.70  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2024,b,2011,b)].
% 12.57/12.70  2025 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(237,a,229,b)].
% 12.57/12.70  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2025,b,2004,b)].
% 12.57/12.70  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2025,b,2007,b)].
% 12.57/12.70  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2025,b,2008,b)].
% 12.57/12.70  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2025,b,2009,b)].
% 12.57/12.70  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2025,b,2011,b)].
% 12.57/12.70  2026 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(241,a,229,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2026,c,2004,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2026,c,2007,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2026,c,2008,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2026,c,2009,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2026,c,2011,b)].
% 12.57/12.70  2027 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A).  [resolve(242,a,229,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2027,c,2004,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2027,c,2007,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2027,c,2008,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2027,c,2009,b)].
% 12.57/12.70  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2027,c,2011,b)].
% 12.75/12.92  2028 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint).  [resolve(1135,a,1091,a)].
% 12.75/12.92  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2028,a,2000,a)].
% 12.75/12.92  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2028,a,2013,a)].
% 12.75/12.92  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2028,a,2018,a)].
% 12.75/12.92  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2028,a,2019,a)].
% 12.75/12.92  2029 class_Ring__and__Field_Opordered__semiring(tc_nat).  [resolve(1135,a,1116,a)].
% 12.75/12.92  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2029,a,2000,a)].
% 12.75/12.92  Derived: class_HOL_Otimes(tc_nat).  [resolve(2029,a,2013,a)].
% 12.75/12.92  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2029,a,2014,a)].
% 12.75/12.92  Derived: class_HOL_Ozero(tc_nat).  [resolve(2029,a,2017,a)].
% 12.75/12.92  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(2029,a,2018,a)].
% 12.75/12.92  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(2029,a,2019,a)].
% 12.75/12.92  2030 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1135,a,1117,b)].
% 12.75/12.92  2031 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1135,a,1118,b)].
% 12.75/12.92  2032 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A).  [resolve(1573,b,1542,a)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2032,a,2003,b)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2032,a,2008,b)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2032,a,2009,b)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2032,a,2010,b)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2032,a,2011,b)].
% 12.75/12.92  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2032,a,2012,b)].
% 12.75/12.92  2033 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1573,b,1543,a)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2033,a,2003,b)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2033,a,2008,b)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2033,a,2009,b)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2033,a,2010,b)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2033,a,2011,b)].
% 12.75/12.92  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2033,a,2012,b)].
% 12.75/12.92  2034 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1573,b,1544,a)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2034,a,2003,b)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2034,a,2008,b)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2034,a,2009,b)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2034,a,2010,b)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2034,a,2011,b)].
% 12.75/12.92  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2034,a,2012,b)].
% 12.75/12.92  2035 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1573,b,1545,a)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2035,a,2003,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2035,a,2008,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2035,a,2009,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2035,a,2010,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2035,a,2011,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2035,a,2012,b)].
% 12.75/12.92  2036 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1573,b,1546,a)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2036,a,2003,b)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2036,a,2008,b)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2036,a,2009,b)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2036,a,2010,b)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2036,a,2011,b)].
% 12.75/12.92  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2036,a,2012,b)].
% 12.75/12.92  2037 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1573,b,1547,a)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2037,a,2003,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2037,a,2008,b)].
% 12.75/12.92  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2037,a,2009,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2037,a,2010,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2037,a,2011,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2037,a,2012,b)].
% 12.75/12.93  2038 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1573,b,1548,a)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2038,a,2003,b)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2038,a,2008,b)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2038,a,2009,b)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2038,a,2010,b)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2038,a,2011,b)].
% 12.75/12.93  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2038,a,2012,b)].
% 12.75/12.93  2039 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1573,b,1549,a)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2039,a,2003,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2039,a,2008,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2039,a,2009,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2039,a,2010,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2039,a,2011,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2039,a,2012,b)].
% 12.75/12.93  2040 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1573,b,1550,a)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2040,a,2003,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2040,a,2008,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2040,a,2009,b)].
% 12.75/12.93  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2040,a,2010,b)].
% 12.84/12.98  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2040,a,2011,b)].
% 12.84/12.98  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2040,a,2012,b)].
% 12.84/12.98  2041 -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1573,b,1551,a)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2041,a,2003,b)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2041,a,2008,b)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2041,a,2009,b)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2041,a,2010,b)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2041,a,2011,b)].
% 12.84/12.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2041,a,2012,b)].
% 12.84/12.98  2042 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A).  [resolve(1573,b,1552,a)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2042,a,2003,b)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2042,a,2008,b)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2042,a,2009,b)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2042,a,2010,b)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2042,a,2011,b)].
% 12.84/12.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2042,a,2012,b)].
% 12.84/12.98  2043 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1596,a)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2043,a,2003,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2043,a,2008,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2043,a,2009,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2043,a,2010,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2043,a,2011,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2043,a,2012,b)].
% 12.84/12.98  2044 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1636,b,1597,a)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2044,a,2003,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2044,a,2008,b)].
% 12.84/12.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2044,a,2009,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2044,a,2010,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2044,a,2011,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2044,a,2012,b)].
% 12.84/12.99  2045 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1636,b,1598,a)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2045,a,2003,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2045,a,2008,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2045,a,2009,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2045,a,2010,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2045,a,2011,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2045,a,2012,b)].
% 12.84/12.99  2046 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1599,a)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2046,a,2003,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2046,a,2008,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2046,a,2009,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2046,a,2010,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2046,a,2011,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2046,a,2012,b)].
% 12.84/12.99  2047 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1636,b,1600,a)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2047,a,2003,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2047,a,2008,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2047,a,2009,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2047,a,2010,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2047,a,2011,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2047,a,2012,b)].
% 12.84/12.99  2048 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1636,b,1601,a)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2048,a,2003,b)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2048,a,2008,b)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2048,a,2009,b)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2048,a,2010,b)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2048,a,2011,b)].
% 12.84/12.99  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2048,a,2012,b)].
% 12.84/12.99  2049 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1636,b,1602,a)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2049,a,2003,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2049,a,2008,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2049,a,2009,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2049,a,2010,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2049,a,2011,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2049,a,2012,b)].
% 12.84/12.99  2050 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1636,b,1603,a)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2050,a,2003,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2050,a,2008,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2050,a,2009,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2050,a,2010,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2050,a,2011,b)].
% 12.84/12.99  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2050,a,2012,b)].
% 12.84/12.99  2051 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1636,b,1604,a)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2051,a,2003,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2051,a,2008,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2051,a,2009,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2051,a,2010,b)].
% 12.84/12.99  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2051,a,2011,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2051,a,2012,b)].
% 12.84/13.00  2052 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1636,b,1605,a)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2052,a,2003,b)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2052,a,2008,b)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2052,a,2009,b)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2052,a,2010,b)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2052,a,2011,b)].
% 12.84/13.00  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2052,a,2012,b)].
% 12.84/13.00  2053 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1636,b,1606,a)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2053,a,2003,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2053,a,2008,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2053,a,2009,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2053,a,2010,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2053,a,2011,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2053,a,2012,b)].
% 12.84/13.00  2054 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1636,b,1607,a)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2054,a,2003,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2054,a,2008,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2054,a,2009,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2054,a,2010,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2054,a,2011,b)].
% 12.84/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2054,a,2012,b)].
% 12.84/13.00  2055 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1636,b,1608,a)].
% 12.84/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2055,a,2003,b)].
% 12.84/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2055,a,2008,b)].
% 12.84/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2055,a,2009,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2055,a,2010,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2055,a,2011,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2055,a,2012,b)].
% 12.88/13.00  2056 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1636,b,1609,a)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2056,a,2003,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2056,a,2008,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2056,a,2009,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2056,a,2010,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2056,a,2011,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2056,a,2012,b)].
% 12.88/13.00  2057 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1636,b,1610,a)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2057,a,2003,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2057,a,2008,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2057,a,2009,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2057,a,2010,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2057,a,2011,b)].
% 12.88/13.00  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2057,a,2012,b)].
% 12.88/13.00  2058 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1636,b,1611,a)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2058,a,2003,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2058,a,2008,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2058,a,2009,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2058,a,2010,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2058,a,2011,b)].
% 12.88/13.00  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2058,a,2012,b)].
% 12.88/13.00  2059 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1636,b,1612,a)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2059,a,2003,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2059,a,2008,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2059,a,2009,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2059,a,2010,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2059,a,2011,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2059,a,2012,b)].
% 13.04/13.23  2060 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1636,b,1613,a)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2060,a,2003,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2060,a,2008,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2060,a,2009,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2060,a,2010,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2060,a,2011,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2060,a,2012,b)].
% 13.04/13.23  2061 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1636,b,1614,a)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2061,a,2003,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2061,a,2008,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2061,a,2009,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2061,a,2010,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2061,a,2011,b)].
% 13.04/13.23  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2061,a,2012,b)].
% 13.04/13.23  2062 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1636,b,1615,a)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2062,a,2003,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2062,a,2008,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2062,a,2009,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2062,a,2010,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2062,a,2011,b)].
% 13.04/13.23  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2062,a,2012,b)].
% 13.04/13.23  2063 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_10) # label(axiom).  [assumption].
% 13.13/13.25  2064 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom).  [assumption].
% 13.13/13.25  2065 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom).  [assumption].
% 13.13/13.25  2066 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_7) # label(axiom).  [assumption].
% 13.13/13.25  2067 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) # label(axiom).  [assumption].
% 13.13/13.25  2068 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_45) # label(axiom).  [assumption].
% 13.13/13.25  2069 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_40) # label(axiom).  [assumption].
% 13.13/13.25  2070 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_22) # label(axiom).  [assumption].
% 13.13/13.25  2071 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) # label(axiom).  [assumption].
% 13.13/13.25  2072 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_3) # label(axiom).  [assumption].
% 13.13/13.25  2073 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_4) # label(axiom).  [assumption].
% 13.13/13.25  2074 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_5) # label(axiom).  [assumption].
% 13.13/13.25  2075 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # label(axiom).  [assumption].
% 13.13/13.25  2076 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_9) # label(axiom).  [assumption].
% 13.13/13.25  2077 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Opordered__cancel__semiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_22) # label(axiom).  [assumption].
% 13.13/13.25  2078 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(34,b,1,a)].
% 13.13/13.25  2079 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(34,b,3,a)].
% 13.13/13.25  2080 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A).  [resolve(34,b,10,a)].
% 13.13/13.25  2081 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(81,b,72,b)].
% 13.13/13.25  2082 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(155,b,131,b)].
% 13.13/13.25  2083 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(155,b,133,b)].
% 13.13/13.25  2084 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(165,a,155,b)].
% 13.13/13.25  2085 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(166,a,155,b)].
% 13.13/13.25  2086 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(236,a,225,b)].
% 13.34/13.47  2087 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(237,a,225,b)].
% 13.34/13.47  2088 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(241,a,225,b)].
% 13.34/13.47  2089 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(242,a,225,b)].
% 13.34/13.47  2090 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(301,b,280,a)].
% 13.34/13.47  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2090,a,2067,b)].
% 13.34/13.47  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2090,a,2070,b)].
% 13.34/13.47  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2090,a,2071,b)].
% 13.34/13.47  2091 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(301,b,282,a)].
% 13.34/13.47  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2091,a,2067,b)].
% 13.34/13.47  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2091,a,2070,b)].
% 13.34/13.47  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2091,a,2071,b)].
% 13.34/13.47  2092 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(314,a,301,b)].
% 13.34/13.47  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2092,c,2071,b)].
% 13.34/13.47  2093 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(315,a,301,b)].
% 13.34/13.47  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2093,c,2071,b)].
% 13.34/13.47  2094 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(318,a,301,b)].
% 13.34/13.47  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2094,b,2071,b)].
% 13.34/13.47  2095 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(764,a,708,a)].
% 13.34/13.47  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2095,a,2071,b)].
% 13.34/13.47  2096 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint).  [resolve(1133,a,1091,a)].
% 13.34/13.47  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(2096,a,2090,a)].
% 13.34/13.47  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(2096,a,2091,a)].
% 13.34/13.47  2097 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).  [resolve(1133,a,1116,a)].
% 13.34/13.47  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(2097,a,2090,a)].
% 13.34/13.47  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(2097,a,2091,a)].
% 13.34/13.47  2098 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1133,a,1117,b)].
% 13.34/13.47  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0.  [resolve(2098,a,2090,a)].
% 13.34/13.47  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0.  [resolve(2098,a,2091,a)].
% 13.34/13.47  2099 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1133,a,1118,b)].
% 13.34/13.47  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0.  [resolve(2099,a,2090,a)].
% 13.34/13.47  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0.  [resolve(2099,a,2091,a)].
% 13.34/13.47  2100 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A).  [resolve(1569,b,1542,a)].
% 13.34/13.47  2101 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1569,b,1543,a)].
% 13.34/13.47  2102 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1569,b,1544,a)].
% 13.34/13.53  2103 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1569,b,1545,a)].
% 13.34/13.53  2104 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1569,b,1546,a)].
% 13.34/13.53  2105 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1569,b,1547,a)].
% 13.34/13.53  2106 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1569,b,1548,a)].
% 13.34/13.53  2107 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1569,b,1549,a)].
% 13.34/13.53  2108 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1569,b,1550,a)].
% 13.34/13.53  2109 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1569,b,1551,a)].
% 13.34/13.53  2110 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A).  [resolve(1569,b,1552,a)].
% 13.34/13.53  2111 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1596,a)].
% 13.34/13.53  2112 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1632,b,1597,a)].
% 13.34/13.53  2113 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1632,b,1598,a)].
% 13.34/13.53  2114 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1599,a)].
% 13.34/13.53  2115 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1632,b,1600,a)].
% 13.34/13.53  2116 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1632,b,1601,a)].
% 13.34/13.53  2117 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1632,b,1602,a)].
% 13.34/13.53  2118 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1632,b,1603,a)].
% 13.34/13.53  2119 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1632,b,1604,a)].
% 13.34/13.53  2120 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1632,b,1605,a)].
% 13.34/13.53  2121 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1632,b,1606,a)].
% 13.34/13.53  2122 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1632,b,1607,a)].
% 13.34/13.53  2123 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1632,b,1608,a)].
% 13.34/13.53  2124 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1632,b,1609,a)].
% 13.34/13.53  2125 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1632,b,1610,a)].
% 13.34/13.53  2126 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1632,b,1611,a)].
% 13.34/13.53  2127 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1632,b,1612,a)].
% 13.48/13.61  2128 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1632,b,1613,a)].
% 13.48/13.61  2129 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1632,b,1614,a)].
% 13.48/13.61  2130 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1632,b,1615,a)].
% 13.48/13.61  2131 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2022,b,2009,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2131,b,2066,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2131,b,2067,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2131,b,2068,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2131,b,2069,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2131,b,2070,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2131,b,2071,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2131,b,2077,b)].
% 13.48/13.61  2132 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2023,b,2009,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2132,b,2066,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2132,b,2067,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2132,b,2068,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2132,b,2069,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2132,b,2070,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2132,b,2071,b)].
% 13.48/13.61  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2132,b,2077,b)].
% 13.48/13.61  2133 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2024,b,2009,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2133,b,2064,a)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2133,b,2066,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2133,b,2067,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2133,b,2068,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2133,b,2069,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2133,b,2070,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2133,b,2071,b)].
% 13.48/13.61  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2133,b,2077,b)].
% 13.48/13.61  2134 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2025,b,2009,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2134,b,2064,a)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2134,b,2066,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2134,b,2067,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2134,b,2068,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2134,b,2069,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2134,b,2070,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2134,b,2071,b)].
% 13.48/13.61  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2134,b,2077,b)].
% 13.48/13.61  2135 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2026,c,2009,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2135,c,2066,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2135,c,2067,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2135,c,2068,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2135,c,2069,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2135,c,2070,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2135,c,2071,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2135,c,2077,b)].
% 13.48/13.61  2136 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A).  [resolve(2027,c,2009,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2136,c,2066,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2136,c,2067,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2136,c,2068,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2136,c,2069,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2136,c,2070,b)].
% 13.48/13.61  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2136,c,2071,b)].
% 13.48/13.62  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2136,c,2077,b)].
% 13.48/13.62  2137 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2032,a,2009,b)].
% 13.48/13.62  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2137,b,2064,a)].
% 13.48/13.62  Derived: -c_less(A,A,tc_nat).  [resolve(2137,b,2065,a)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2137,b,2066,b)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2137,b,2067,b)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2137,b,2068,b)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2137,b,2069,b)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2137,b,2070,b)].
% 13.48/13.62  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2137,b,2071,b)].
% 13.48/13.62  2138 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2033,a,2009,b)].
% 13.48/13.62  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2138,c,2064,a)].
% 13.48/13.62  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2138,c,2065,a)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2138,c,2066,b)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2138,c,2067,b)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2138,c,2068,b)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2138,c,2069,b)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2138,c,2070,b)].
% 13.48/13.62  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2138,c,2071,b)].
% 13.48/13.62  2139 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2034,a,2009,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2139,b,2064,a)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2139,b,2065,a)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2139,b,2066,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2139,b,2067,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2139,b,2068,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2139,b,2069,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2139,b,2070,b)].
% 13.48/13.62  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2139,b,2071,b)].
% 13.48/13.62  2140 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2035,a,2009,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2140,c,2064,a)].
% 13.48/13.62  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2140,c,2065,a)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2140,c,2066,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2140,c,2067,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2140,c,2068,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2140,c,2069,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2140,c,2070,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2140,c,2071,b)].
% 13.48/13.62  2141 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2036,a,2009,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2141,c,2064,a)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(2141,c,2065,a)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2141,c,2066,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2141,c,2067,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2141,c,2068,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2141,c,2069,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2141,c,2070,b)].
% 13.48/13.62  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2141,c,2071,b)].
% 13.48/13.62  2142 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2037,a,2009,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2142,c,2064,a)].
% 13.48/13.62  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(2142,c,2065,a)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2142,c,2066,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2142,c,2067,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2142,c,2068,b)].
% 13.48/13.62  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2142,c,2069,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2142,c,2070,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2142,c,2071,b)].
% 13.48/13.63  2143 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2038,a,2009,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2143,c,2064,a)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(2143,c,2065,a)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2143,c,2066,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2143,c,2067,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2143,c,2068,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2143,c,2069,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2143,c,2070,b)].
% 13.48/13.63  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2143,c,2071,b)].
% 13.48/13.63  2144 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2039,a,2009,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2144,c,2064,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(2144,c,2065,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2144,c,2066,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2144,c,2067,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2144,c,2068,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2144,c,2069,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2144,c,2070,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2144,c,2071,b)].
% 13.48/13.63  2145 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2040,a,2009,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2145,c,2064,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2145,c,2065,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2145,c,2066,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2145,c,2067,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2145,c,2068,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2145,c,2069,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2145,c,2070,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2145,c,2071,b)].
% 13.48/13.63  2146 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2041,a,2009,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2146,b,2064,a)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(2146,b,2065,a)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2146,b,2066,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2146,b,2067,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2146,b,2068,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2146,b,2069,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2146,b,2070,b)].
% 13.48/13.63  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2146,b,2071,b)].
% 13.48/13.63  2147 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B).  [resolve(2042,a,2009,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2147,b,2064,a)].
% 13.48/13.63  Derived: c_lessequals(A,A,tc_nat).  [resolve(2147,b,2065,a)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2147,b,2066,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2147,b,2067,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2147,b,2068,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2147,b,2069,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2147,b,2070,b)].
% 13.48/13.63  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2147,b,2071,b)].
% 13.48/13.63  2148 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2043,a,2009,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2148,c,2064,a)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2148,c,2065,a)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2148,c,2066,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2148,c,2067,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2148,c,2068,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2148,c,2069,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2148,c,2070,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2148,c,2071,b)].
% 13.48/13.63  2149 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2044,a,2009,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2149,c,2064,a)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2149,c,2065,a)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2149,c,2066,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2149,c,2067,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2149,c,2068,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2149,c,2069,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2149,c,2070,b)].
% 13.48/13.63  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2149,c,2071,b)].
% 13.48/13.63  2150 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2045,a,2009,b)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2150,d,2064,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(2150,d,2065,a)].
% 13.48/13.63  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2150,d,2066,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2150,d,2067,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2150,d,2068,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2150,d,2069,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2150,d,2070,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2150,d,2071,b)].
% 13.48/13.64  2151 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2046,a,2009,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2151,c,2064,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2151,c,2065,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2151,c,2066,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2151,c,2067,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2151,c,2068,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2151,c,2069,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2151,c,2070,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2151,c,2071,b)].
% 13.48/13.64  2152 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2047,a,2009,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2152,c,2064,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2152,c,2065,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2152,c,2066,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2152,c,2067,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2152,c,2068,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2152,c,2069,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2152,c,2070,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2152,c,2071,b)].
% 13.48/13.64  2153 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2048,a,2009,b)].
% 13.48/13.64  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2153,d,2064,a)].
% 13.48/13.64  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(2153,d,2065,a)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2153,d,2066,b)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2153,d,2067,b)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2153,d,2068,b)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2153,d,2069,b)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2153,d,2070,b)].
% 13.48/13.64  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2153,d,2071,b)].
% 13.48/13.64  2154 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2049,a,2009,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2154,c,2064,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2154,c,2065,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2154,c,2066,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2154,c,2067,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2154,c,2068,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2154,c,2069,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2154,c,2070,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2154,c,2071,b)].
% 13.48/13.64  2155 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2050,a,2009,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2155,c,2064,a)].
% 13.48/13.64  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2155,c,2065,a)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2155,c,2066,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2155,c,2067,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2155,c,2068,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2155,c,2069,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2155,c,2070,b)].
% 13.48/13.64  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2155,c,2071,b)].
% 13.48/13.64  2156 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2051,a,2009,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2156,c,2064,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2156,c,2065,a)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2156,c,2066,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2156,c,2067,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2156,c,2068,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2156,c,2069,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2156,c,2070,b)].
% 13.48/13.64  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2156,c,2071,b)].
% 13.54/13.65  2157 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2052,a,2009,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2157,c,2064,a)].
% 13.54/13.65  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2157,c,2065,a)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2157,c,2066,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2157,c,2067,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2157,c,2068,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2157,c,2069,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2157,c,2070,b)].
% 13.54/13.65  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2157,c,2071,b)].
% 13.54/13.65  2158 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2053,a,2009,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2158,c,2064,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2158,c,2065,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2158,c,2066,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2158,c,2067,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2158,c,2068,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2158,c,2069,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2158,c,2070,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2158,c,2071,b)].
% 13.54/13.65  2159 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2054,a,2009,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2159,c,2064,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2159,c,2065,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2159,c,2066,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2159,c,2067,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2159,c,2068,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2159,c,2069,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2159,c,2070,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2159,c,2071,b)].
% 13.54/13.65  2160 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2055,a,2009,b)].
% 13.54/13.65  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2160,d,2064,a)].
% 13.54/13.65  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(2160,d,2065,a)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2160,d,2066,b)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2160,d,2067,b)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2160,d,2068,b)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2160,d,2069,b)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2160,d,2070,b)].
% 13.54/13.65  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2160,d,2071,b)].
% 13.54/13.65  2161 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2056,a,2009,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2161,c,2064,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2161,c,2065,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2161,c,2066,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2161,c,2067,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2161,c,2068,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2161,c,2069,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2161,c,2070,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2161,c,2071,b)].
% 13.54/13.65  2162 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D).  [resolve(2057,a,2009,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2162,c,2064,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2162,c,2065,a)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2162,c,2066,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2162,c,2067,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2162,c,2068,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2162,c,2069,b)].
% 13.54/13.65  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2162,c,2070,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2162,c,2071,b)].
% 13.54/13.66  2163 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2058,a,2009,b)].
% 13.54/13.66  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2163,d,2064,a)].
% 13.54/13.66  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(2163,d,2065,a)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2163,d,2066,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2163,d,2067,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2163,d,2068,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2163,d,2069,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2163,d,2070,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2163,d,2071,b)].
% 13.54/13.66  2164 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2059,a,2009,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2164,c,2064,a)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2164,c,2065,a)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2164,c,2066,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2164,c,2067,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2164,c,2068,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2164,c,2069,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2164,c,2070,b)].
% 13.54/13.66  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2164,c,2071,b)].
% 13.54/13.66  2165 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2060,a,2009,b)].
% 13.54/13.66  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2165,c,2064,a)].
% 13.54/13.66  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2165,c,2065,a)].
% 13.54/13.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2165,c,2066,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2165,c,2067,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2165,c,2068,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2165,c,2069,b)].
% 13.54/13.66  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2165,c,2070,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2165,c,2071,b)].
% 13.74/13.84  2166 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2061,a,2009,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(2166,c,2064,a)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2166,c,2065,a)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2166,c,2066,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2166,c,2067,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2166,c,2068,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2166,c,2069,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2166,c,2070,b)].
% 13.74/13.84  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2166,c,2071,b)].
% 13.74/13.84  2167 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C).  [resolve(2062,a,2009,b)].
% 13.74/13.84  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2167,c,2064,a)].
% 13.74/13.84  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2167,c,2065,a)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2167,c,2066,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2167,c,2067,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2167,c,2068,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2167,c,2069,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2167,c,2070,b)].
% 13.74/13.84  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2167,c,2071,b)].
% 13.74/13.84  2168 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_2) # label(axiom).  [assumption].
% 13.74/13.84  2169 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom).  [assumption].
% 13.74/13.84  2170 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom).  [assumption].
% 13.74/13.84  2171 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) # label(axiom).  [assumption].
% 13.74/13.84  2172 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_39) # label(axiom).  [assumption].
% 13.74/13.84  2173 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_31) # label(axiom).  [assumption].
% 13.74/13.84  2174 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_3) # label(axiom).  [assumption].
% 13.74/13.84  2175 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_4) # label(axiom).  [assumption].
% 13.79/13.93  2176 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_6) # label(axiom).  [assumption].
% 13.79/13.93  2177 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_7) # label(axiom).  [assumption].
% 13.79/13.93  2178 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_8) # label(axiom).  [assumption].
% 13.79/13.93  2179 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(32,b,1,a)].
% 13.79/13.93  2180 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(32,b,3,a)].
% 13.79/13.93  2181 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(81,b,70,b)].
% 13.79/13.93  2182 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(82,b,70,b)].
% 13.79/13.93  2183 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(153,b,131,b)].
% 13.79/13.93  2184 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(153,b,133,b)].
% 13.79/13.93  2185 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(165,a,153,b)].
% 13.79/13.93  2186 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(166,a,153,b)].
% 13.79/13.93  2187 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(236,a,223,b)].
% 13.79/13.93  2188 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(237,a,223,b)].
% 13.79/13.93  2189 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(241,a,223,b)].
% 13.79/13.93  2190 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(242,a,223,b)].
% 13.79/13.93  2191 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(299,b,280,a)].
% 13.79/13.93  2192 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(299,b,282,a)].
% 13.79/13.93  2193 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(314,a,299,b)].
% 13.79/13.93  2194 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(315,a,299,b)].
% 13.79/13.93  2195 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(763,a,708,a)].
% 13.79/13.93  2196 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(763,a,715,a)].
% 13.79/13.93  2197 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(876,b,806,a)].
% 13.79/13.93  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2197,a,2171,b)].
% 13.79/13.93  2198 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(876,b,807,a)].
% 13.79/13.93  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2198,a,2171,b)].
% 13.79/13.93  2199 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(876,b,808,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2199,a,2171,b)].
% 13.79/13.94  2200 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(876,b,809,a)].
% 13.79/13.94  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2200,a,2171,b)].
% 13.79/13.94  2201 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,810,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2201,a,2171,b)].
% 13.79/13.94  2202 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,811,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2202,a,2171,b)].
% 13.79/13.94  2203 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(876,b,812,a)].
% 13.79/13.94  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2203,a,2171,b)].
% 13.79/13.94  2204 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,813,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2204,a,2171,b)].
% 13.79/13.94  2205 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(876,b,814,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2205,a,2171,b)].
% 13.79/13.94  2206 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(876,b,815,a)].
% 13.79/13.94  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2206,a,2171,b)].
% 13.79/13.94  2207 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(876,b,816,a)].
% 13.79/13.94  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2207,a,2171,b)].
% 13.79/13.94  2208 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,817,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2208,a,2171,b)].
% 13.79/13.94  2209 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,818,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2209,a,2171,b)].
% 13.79/13.94  2210 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(876,b,819,a)].
% 13.79/13.94  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2210,a,2171,b)].
% 13.79/13.94  2211 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,820,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2211,a,2171,b)].
% 13.79/13.94  2212 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(876,b,821,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2212,a,2171,b)].
% 13.79/13.94  2213 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(876,b,822,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2213,a,2171,b)].
% 13.79/13.94  2214 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(876,b,823,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2214,a,2171,b)].
% 13.79/13.94  2215 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(876,b,824,a)].
% 13.79/13.94  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2215,a,2171,b)].
% 13.79/13.94  2216 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(876,b,825,a)].
% 13.79/13.94  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2216,a,2171,b)].
% 13.79/13.94  2217 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(876,b,826,a)].
% 13.79/13.94  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2217,a,2171,b)].
% 13.84/13.95  2218 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(876,b,827,a)].
% 13.84/13.95  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2218,a,2171,b)].
% 13.84/13.95  2219 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(876,b,828,a)].
% 13.84/13.95  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2219,a,2171,b)].
% 13.84/13.95  2220 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(876,b,829,b)].
% 13.84/13.95  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2220,a,2171,b)].
% 13.84/13.95  2221 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(876,b,830,b)].
% 13.84/13.95  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2221,a,2171,b)].
% 13.84/13.95  2222 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(876,b,831,a)].
% 13.84/13.95  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2222,a,2171,b)].
% 13.84/13.95  2223 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(876,b,832,a)].
% 13.84/13.95  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2223,a,2171,b)].
% 13.84/13.95  2224 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(876,b,833,a)].
% 13.84/13.95  Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2224,a,2171,b)].
% 13.84/13.95  2225 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(876,b,834,a)].
% 13.84/13.95  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2225,a,2171,b)].
% 13.84/13.95  2226 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(876,b,835,a)].
% 13.84/13.95  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2226,a,2171,b)].
% 13.84/13.95  2227 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(876,b,836,a)].
% 13.84/13.95  Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2227,a,2171,b)].
% 13.84/13.95  2228 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(876,b,837,a)].
% 13.84/13.95  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2228,a,2171,b)].
% 13.84/13.95  2229 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(876,b,838,a)].
% 13.84/13.96  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2229,a,2171,b)].
% 13.84/13.96  2230 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(876,b,839,a)].
% 13.84/13.96  Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2230,a,2171,b)].
% 13.84/13.96  2231 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(876,b,840,a)].
% 13.84/13.96  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2231,a,2171,b)].
% 13.84/13.96  2232 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(876,b,841,a)].
% 13.84/13.96  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2232,a,2171,b)].
% 13.84/13.96  2233 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(876,b,842,a)].
% 13.84/13.96  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2233,a,2171,b)].
% 13.84/13.96  2234 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(876,b,843,a)].
% 13.84/13.96  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2234,a,2171,b)].
% 13.84/13.96  2235 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(876,b,844,a)].
% 13.84/13.96  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2235,a,2171,b)].
% 13.84/13.96  2236 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(876,b,845,a)].
% 13.84/13.96  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2236,a,2171,b)].
% 13.84/13.96  2237 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(876,b,846,a)].
% 13.84/13.96  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2237,a,2171,b)].
% 13.84/13.96  2238 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(876,b,847,a)].
% 13.84/13.96  Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2238,a,2171,b)].
% 13.84/13.96  2239 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(876,b,848,a)].
% 13.84/13.96  Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2239,a,2171,b)].
% 13.84/13.96  2240 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(876,b,849,a)].
% 13.84/13.96  Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2240,a,2171,b)].
% 13.84/13.96  2241 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(876,b,850,a)].
% 13.84/13.96  Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2241,a,2171,b)].
% 13.84/13.97  2242 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(876,b,851,a)].
% 13.84/13.97  Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2242,a,2171,b)].
% 13.84/13.97  2243 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(876,b,852,a)].
% 13.84/13.97  Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2243,a,2171,b)].
% 13.84/13.97  2244 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(876,b,853,a)].
% 13.84/13.97  Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2244,a,2171,b)].
% 13.84/13.97  2245 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(876,b,854,a)].
% 13.84/13.97  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2245,a,2171,b)].
% 13.84/13.97  2246 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(876,b,855,a)].
% 13.84/13.97  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2246,a,2171,b)].
% 13.84/13.97  2247 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(876,b,856,a)].
% 13.84/13.97  Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2247,a,2171,b)].
% 13.84/13.97  2248 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(876,b,857,a)].
% 13.84/13.97  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2248,a,2171,b)].
% 13.84/13.97  2249 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(876,b,858,a)].
% 13.84/13.97  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2249,a,2171,b)].
% 13.84/13.97  2250 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(876,b,859,a)].
% 13.84/13.97  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2250,a,2171,b)].
% 13.84/13.97  2251 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(876,b,860,a)].
% 13.84/13.97  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2251,a,2171,b)].
% 13.94/14.09  2252 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(876,b,861,a)].
% 13.94/14.09  Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2252,a,2171,b)].
% 13.94/14.09  2253 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(876,b,862,a)].
% 13.94/14.09  Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2253,a,2171,b)].
% 13.94/14.09  2254 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(876,b,863,a)].
% 13.94/14.09  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2254,a,2171,b)].
% 13.94/14.09  2255 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1062,b,1046,a)].
% 13.94/14.09  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2255,a,2171,b)].
% 13.94/14.09  2256 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1085,b,1069,a)].
% 13.94/14.09  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2256,a,2171,b)].
% 13.94/14.09  2257 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint).  [resolve(1127,a,1091,a)].
% 13.94/14.09  2258 class_Ring__and__Field_Oordered__semiring__strict(tc_nat).  [resolve(1127,a,1116,a)].
% 13.94/14.09  2259 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1127,a,1117,b)].
% 13.94/14.09  2260 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1127,a,1118,b)].
% 13.94/14.09  2261 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1462,b,1438,a)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2261,a,2171,b)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2261,a,2172,b)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2261,a,2173,b)].
% 13.94/14.09  2262 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1462,b,1439,a)].
% 13.94/14.09  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2262,a,2171,b)].
% 13.94/14.09  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2262,a,2172,b)].
% 13.94/14.09  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2262,a,2173,b)].
% 13.94/14.09  2263 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1462,b,1440,a)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2263,a,2171,b)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2263,a,2172,b)].
% 13.94/14.09  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2263,a,2173,b)].
% 13.94/14.09  2264 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1462,b,1441,a)].
% 13.99/14.14  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2264,a,2171,b)].
% 13.99/14.14  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2264,a,2172,b)].
% 13.99/14.14  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2264,a,2173,b)].
% 13.99/14.14  2265 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1462,b,1442,a)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2265,a,2171,b)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2265,a,2172,b)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2265,a,2173,b)].
% 13.99/14.14  2266 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1462,b,1443,a)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2266,a,2171,b)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2266,a,2172,b)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2266,a,2173,b)].
% 13.99/14.14  2267 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1462,b,1444,a)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2267,a,2171,b)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2267,a,2172,b)].
% 13.99/14.14  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2267,a,2173,b)].
% 13.99/14.14  2268 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1462,b,1445,a)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2268,a,2171,b)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2268,a,2172,b)].
% 13.99/14.14  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2268,a,2173,b)].
% 13.99/14.14  2269 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A).  [resolve(1567,b,1542,a)].
% 13.99/14.14  2270 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1567,b,1543,a)].
% 13.99/14.14  2271 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1567,b,1544,a)].
% 13.99/14.14  2272 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1567,b,1545,a)].
% 13.99/14.14  2273 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1567,b,1546,a)].
% 13.99/14.14  2274 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1567,b,1547,a)].
% 13.99/14.14  2275 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1567,b,1548,a)].
% 13.99/14.14  2276 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1567,b,1549,a)].
% 14.10/14.24  2277 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1567,b,1550,a)].
% 14.10/14.24  2278 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1567,b,1551,a)].
% 14.10/14.24  2279 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1567,b,1552,a)].
% 14.10/14.24  2280 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1596,a)].
% 14.10/14.24  2281 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1630,b,1597,a)].
% 14.10/14.24  2282 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1630,b,1598,a)].
% 14.10/14.24  2283 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1599,a)].
% 14.10/14.24  2284 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1630,b,1600,a)].
% 14.10/14.24  2285 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1630,b,1601,a)].
% 14.10/14.24  2286 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1630,b,1602,a)].
% 14.10/14.24  2287 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1630,b,1603,a)].
% 14.10/14.24  2288 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1630,b,1604,a)].
% 14.10/14.24  2289 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1630,b,1605,a)].
% 14.10/14.24  2290 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1630,b,1606,a)].
% 14.10/14.24  2291 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1630,b,1607,a)].
% 14.10/14.24  2292 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1630,b,1608,a)].
% 14.10/14.24  2293 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1630,b,1609,a)].
% 14.10/14.24  2294 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1630,b,1610,a)].
% 14.10/14.24  2295 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1630,b,1611,a)].
% 14.10/14.24  2296 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1630,b,1612,a)].
% 14.10/14.24  2297 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1630,b,1613,a)].
% 14.10/14.24  2298 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1630,b,1614,a)].
% 14.10/14.24  2299 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1630,b,1615,a)].
% 14.10/14.24  2300 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1934,c,1857,b)].
% 14.10/14.24  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(2300,c,2169,a)].
% 14.10/14.24  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(2300,c,2170,a)].
% 14.10/14.24  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2300,c,2171,b)].
% 14.10/14.24  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(2300,c,2172,b)].
% 14.14/14.26  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2300,c,2173,b)].
% 14.14/14.26  2301 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1935,c,1857,b)].
% 14.14/14.26  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(2301,c,2169,a)].
% 14.14/14.26  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(2301,c,2170,a)].
% 14.14/14.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2301,c,2171,b)].
% 14.14/14.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C).  [resolve(2301,c,2172,b)].
% 14.14/14.26  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2301,c,2173,b)].
% 14.14/14.26  2302 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1936,b,1857,b)].
% 14.14/14.26  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(2302,b,2169,a)].
% 14.14/14.26  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(2302,b,2170,a)].
% 14.14/14.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2302,b,2171,b)].
% 14.14/14.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2302,b,2172,b)].
% 14.14/14.26  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2302,b,2173,b)].
% 14.14/14.26  2303 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(1937,b,1857,b)].
% 14.14/14.26  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(2303,b,2169,a)].
% 14.14/14.26  Derived: class_HOL_Oplus(tc_nat).  [resolve(2303,b,2170,a)].
% 14.14/14.26  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2303,b,2171,b)].
% 14.14/14.26  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2303,b,2172,b)].
% 14.14/14.26  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2303,b,2173,b)].
% 14.14/14.26  2304 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1969,b,1857,b)].
% 14.14/14.26  2305 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1970,c,1857,b)].
% 14.14/14.26  2306 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1971,b,1857,b)].
% 14.14/14.26  2307 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1972,c,1857,b)].
% 14.14/14.26  2308 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1973,c,1857,b)].
% 14.14/14.26  2309 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1974,c,1857,b)].
% 14.14/14.26  2310 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1975,c,1857,b)].
% 14.14/14.26  2311 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1976,c,1857,b)].
% 14.14/14.26  2312 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1977,c,1857,b)].
% 14.14/14.26  2313 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1978,b,1857,b)].
% 14.14/14.26  2314 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(1979,b,1857,b)].
% 14.14/14.26  2315 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1980,c,1857,b)].
% 14.14/14.33  2316 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1981,c,1857,b)].
% 14.14/14.33  2317 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1982,d,1857,b)].
% 14.14/14.33  2318 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1983,c,1857,b)].
% 14.14/14.33  2319 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1984,c,1857,b)].
% 14.14/14.33  2320 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1985,d,1857,b)].
% 14.14/14.33  2321 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1986,c,1857,b)].
% 14.14/14.33  2322 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1987,c,1857,b)].
% 14.14/14.33  2323 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1988,c,1857,b)].
% 14.14/14.33  2324 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1989,c,1857,b)].
% 14.14/14.33  2325 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1990,c,1857,b)].
% 14.14/14.33  2326 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1991,c,1857,b)].
% 14.14/14.33  2327 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1992,d,1857,b)].
% 14.14/14.33  2328 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1993,c,1857,b)].
% 14.14/14.33  2329 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(1994,c,1857,b)].
% 14.14/14.33  2330 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1995,d,1857,b)].
% 14.14/14.33  2331 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1996,c,1857,b)].
% 14.14/14.33  2332 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1997,c,1857,b)].
% 14.14/14.33  2333 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1998,c,1857,b)].
% 14.14/14.33  2334 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(1999,c,1857,b)].
% 14.14/14.33  2335 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2022,b,2007,b)].
% 14.14/14.33  2336 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2023,b,2007,b)].
% 14.14/14.33  2337 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2024,b,2007,b)].
% 14.14/14.33  2338 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2025,b,2007,b)].
% 14.14/14.33  2339 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2026,c,2007,b)].
% 14.14/14.33  2340 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2027,c,2007,b)].
% 14.14/14.33  2341 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2090,a,2070,b)].
% 14.23/14.34  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2341,b,2171,b)].
% 14.23/14.34  2342 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2091,a,2070,b)].
% 14.23/14.34  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2342,b,2171,b)].
% 14.23/14.34  2343 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2131,b,2070,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2343,b,2169,a)].
% 14.23/14.34  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2343,b,2170,a)].
% 14.23/14.34  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2343,b,2171,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2343,b,2172,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2343,b,2173,b)].
% 14.23/14.34  2344 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2132,b,2070,b)].
% 14.23/14.34  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2344,b,2169,a)].
% 14.23/14.34  Derived: class_HOL_Otimes(tc_nat).  [resolve(2344,b,2170,a)].
% 14.23/14.34  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2344,b,2171,b)].
% 14.23/14.34  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2344,b,2172,b)].
% 14.23/14.34  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2344,b,2173,b)].
% 14.23/14.34  2345 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2133,b,2070,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2345,b,2169,a)].
% 14.23/14.34  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2345,b,2170,a)].
% 14.23/14.34  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2345,b,2171,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2345,b,2172,b)].
% 14.23/14.34  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2345,b,2173,b)].
% 14.23/14.34  2346 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2134,b,2070,b)].
% 14.23/14.34  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2346,b,2169,a)].
% 14.23/14.34  Derived: class_HOL_Ozero(tc_nat).  [resolve(2346,b,2170,a)].
% 14.23/14.34  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2346,b,2171,b)].
% 14.23/14.34  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2346,b,2172,b)].
% 14.23/14.34  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2346,b,2173,b)].
% 14.23/14.34  2347 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2135,c,2070,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2347,c,2169,a)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(2347,c,2170,a)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2347,c,2171,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2347,c,2172,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2347,c,2173,b)].
% 14.23/14.34  2348 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A).  [resolve(2136,c,2070,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2348,c,2169,a)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(2348,c,2170,a)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2348,c,2171,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2348,c,2172,b)].
% 14.23/14.34  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2348,c,2173,b)].
% 14.23/14.34  2349 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2137,b,2070,b)].
% 14.23/14.34  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2349,b,2169,a)].
% 14.23/14.34  Derived: -c_less(A,A,tc_nat).  [resolve(2349,b,2170,a)].
% 14.23/14.34  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2349,b,2171,b)].
% 14.23/14.34  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2349,b,2172,b)].
% 14.23/14.34  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2349,b,2173,b)].
% 14.23/14.34  2350 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2138,c,2070,b)].
% 14.23/14.34  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2350,c,2169,a)].
% 14.23/14.34  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2350,c,2170,a)].
% 14.23/14.34  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2350,c,2171,b)].
% 14.23/14.34  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2350,c,2172,b)].
% 14.23/14.34  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2350,c,2173,b)].
% 14.23/14.34  2351 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2139,b,2070,b)].
% 14.23/14.34  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2351,b,2169,a)].
% 14.23/14.34  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2351,b,2170,a)].
% 14.23/14.34  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2351,b,2171,b)].
% 14.23/14.34  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2351,b,2172,b)].
% 14.23/14.35  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2351,b,2173,b)].
% 14.23/14.35  2352 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2140,c,2070,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2352,c,2169,a)].
% 14.23/14.35  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2352,c,2170,a)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2352,c,2171,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2352,c,2172,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2352,c,2173,b)].
% 14.23/14.35  2353 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2141,c,2070,b)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2353,c,2169,a)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(2353,c,2170,a)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2353,c,2171,b)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2353,c,2172,b)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2353,c,2173,b)].
% 14.23/14.35  2354 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2142,c,2070,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2354,c,2169,a)].
% 14.23/14.35  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(2354,c,2170,a)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2354,c,2171,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2354,c,2172,b)].
% 14.23/14.35  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2354,c,2173,b)].
% 14.23/14.35  2355 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2143,c,2070,b)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2355,c,2169,a)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(2355,c,2170,a)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2355,c,2171,b)].
% 14.23/14.35  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2355,c,2172,b)].
% 14.23/14.36  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2355,c,2173,b)].
% 14.23/14.36  2356 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2144,c,2070,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2356,c,2169,a)].
% 14.23/14.36  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(2356,c,2170,a)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2356,c,2171,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2356,c,2172,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2356,c,2173,b)].
% 14.23/14.36  2357 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2145,c,2070,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2357,c,2169,a)].
% 14.23/14.36  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2357,c,2170,a)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2357,c,2171,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2357,c,2172,b)].
% 14.23/14.36  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2357,c,2173,b)].
% 14.23/14.36  2358 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2146,b,2070,b)].
% 14.23/14.36  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2358,b,2169,a)].
% 14.23/14.36  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(2358,b,2170,a)].
% 14.23/14.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2358,b,2171,b)].
% 14.23/14.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2358,b,2172,b)].
% 14.23/14.36  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2358,b,2173,b)].
% 14.23/14.36  2359 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B).  [resolve(2147,b,2070,b)].
% 14.23/14.36  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2359,b,2169,a)].
% 14.23/14.36  Derived: c_lessequals(A,A,tc_nat).  [resolve(2359,b,2170,a)].
% 14.23/14.36  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2359,b,2171,b)].
% 14.23/14.36  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2359,b,2172,b)].
% 14.23/14.36  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2359,b,2173,b)].
% 14.23/14.36  2360 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2148,c,2070,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2360,c,2169,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2360,c,2170,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2360,c,2171,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2360,c,2172,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2360,c,2173,b)].
% 14.23/14.37  2361 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2149,c,2070,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2361,c,2169,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2361,c,2170,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2361,c,2171,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2361,c,2172,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2361,c,2173,b)].
% 14.23/14.37  2362 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2150,d,2070,b)].
% 14.23/14.37  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2362,d,2169,a)].
% 14.23/14.37  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(2362,d,2170,a)].
% 14.23/14.37  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2362,d,2171,b)].
% 14.23/14.37  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2362,d,2172,b)].
% 14.23/14.37  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2362,d,2173,b)].
% 14.23/14.37  2363 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2151,c,2070,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2363,c,2169,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2363,c,2170,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2363,c,2171,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2363,c,2172,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2363,c,2173,b)].
% 14.23/14.37  2364 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2152,c,2070,b)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2364,c,2169,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2364,c,2170,a)].
% 14.23/14.37  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2364,c,2171,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2364,c,2172,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2364,c,2173,b)].
% 14.23/14.38  2365 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2153,d,2070,b)].
% 14.23/14.38  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2365,d,2169,a)].
% 14.23/14.38  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(2365,d,2170,a)].
% 14.23/14.38  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2365,d,2171,b)].
% 14.23/14.38  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2365,d,2172,b)].
% 14.23/14.38  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2365,d,2173,b)].
% 14.23/14.38  2366 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2154,c,2070,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2366,c,2169,a)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2366,c,2170,a)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2366,c,2171,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2366,c,2172,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2366,c,2173,b)].
% 14.23/14.38  2367 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2155,c,2070,b)].
% 14.23/14.38  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2367,c,2169,a)].
% 14.23/14.38  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2367,c,2170,a)].
% 14.23/14.38  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2367,c,2171,b)].
% 14.23/14.38  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2367,c,2172,b)].
% 14.23/14.38  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2367,c,2173,b)].
% 14.23/14.38  2368 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2156,c,2070,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2368,c,2169,a)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2368,c,2170,a)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2368,c,2171,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2368,c,2172,b)].
% 14.23/14.38  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2368,c,2173,b)].
% 14.23/14.38  2369 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2157,c,2070,b)].
% 14.23/14.38  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2369,c,2169,a)].
% 14.27/14.39  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2369,c,2170,a)].
% 14.27/14.39  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2369,c,2171,b)].
% 14.27/14.39  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2369,c,2172,b)].
% 14.27/14.39  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2369,c,2173,b)].
% 14.27/14.39  2370 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2158,c,2070,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2370,c,2169,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2370,c,2170,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2370,c,2171,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2370,c,2172,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2370,c,2173,b)].
% 14.27/14.39  2371 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2159,c,2070,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2371,c,2169,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2371,c,2170,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2371,c,2171,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2371,c,2172,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2371,c,2173,b)].
% 14.27/14.39  2372 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2160,d,2070,b)].
% 14.27/14.39  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2372,d,2169,a)].
% 14.27/14.39  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(2372,d,2170,a)].
% 14.27/14.39  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2372,d,2171,b)].
% 14.27/14.39  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2372,d,2172,b)].
% 14.27/14.39  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2372,d,2173,b)].
% 14.27/14.39  2373 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2161,c,2070,b)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2373,c,2169,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2373,c,2170,a)].
% 14.27/14.39  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2373,c,2171,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2373,c,2172,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2373,c,2173,b)].
% 14.27/14.40  2374 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D).  [resolve(2162,c,2070,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2374,c,2169,a)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2374,c,2170,a)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2374,c,2171,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2374,c,2172,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2374,c,2173,b)].
% 14.27/14.40  2375 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2163,d,2070,b)].
% 14.27/14.40  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2375,d,2169,a)].
% 14.27/14.40  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(2375,d,2170,a)].
% 14.27/14.40  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2375,d,2171,b)].
% 14.27/14.40  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2375,d,2172,b)].
% 14.27/14.40  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2375,d,2173,b)].
% 14.27/14.40  2376 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2164,c,2070,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2376,c,2169,a)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2376,c,2170,a)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2376,c,2171,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2376,c,2172,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2376,c,2173,b)].
% 14.27/14.40  2377 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2165,c,2070,b)].
% 14.27/14.40  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2377,c,2169,a)].
% 14.27/14.40  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2377,c,2170,a)].
% 14.27/14.40  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2377,c,2171,b)].
% 14.27/14.40  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2377,c,2172,b)].
% 14.27/14.40  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2377,c,2173,b)].
% 14.27/14.40  2378 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2166,c,2070,b)].
% 14.27/14.40  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(2378,c,2169,a)].
% 14.44/14.60  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2378,c,2170,a)].
% 14.44/14.60  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2378,c,2171,b)].
% 14.44/14.60  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2378,c,2172,b)].
% 14.44/14.60  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2378,c,2173,b)].
% 14.44/14.60  2379 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C).  [resolve(2167,c,2070,b)].
% 14.44/14.60  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2379,c,2169,a)].
% 14.44/14.60  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2379,c,2170,a)].
% 14.44/14.60  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2379,c,2171,b)].
% 14.44/14.60  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2379,c,2172,b)].
% 14.44/14.60  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2379,c,2173,b)].
% 14.44/14.60  2380 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_10) # label(axiom).  [assumption].
% 14.44/14.60  2381 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom).  [assumption].
% 14.44/14.60  2382 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom).  [assumption].
% 14.44/14.60  2383 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) # label(axiom).  [assumption].
% 14.44/14.60  2384 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_37) # label(axiom).  [assumption].
% 14.44/14.60  2385 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_41) # label(axiom).  [assumption].
% 14.44/14.60  2386 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) # label(axiom).  [assumption].
% 14.44/14.60  2387 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Ring__and__Field_Opordered__comm__semiring(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_20) # label(axiom).  [assumption].
% 14.44/14.60  2388 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_11) # label(axiom).  [assumption].
% 14.44/14.60  2389 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_5) # label(axiom).  [assumption].
% 14.44/14.60  2390 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_6) # label(axiom).  [assumption].
% 14.44/14.60  2391 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_7) # label(axiom).  [assumption].
% 14.44/14.60  2392 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_9) # label(axiom).  [assumption].
% 14.44/14.60  2393 -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(157,b,131,b)].
% 14.44/14.60  2394 -class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(157,b,133,b)].
% 14.73/14.86  2395 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(163,a,157,b)].
% 14.73/14.86  2396 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(164,a,157,b)].
% 14.73/14.86  2397 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(165,a,157,b)].
% 14.73/14.86  2398 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(166,a,157,b)].
% 14.73/14.86  2399 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(236,a,227,b)].
% 14.73/14.86  2400 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(237,a,227,b)].
% 14.73/14.86  2401 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(241,a,227,b)].
% 14.73/14.86  2402 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(242,a,227,b)].
% 14.73/14.86  2403 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint).  [resolve(1134,a,1091,a)].
% 14.73/14.86  2404 class_Ring__and__Field_Opordered__comm__semiring(tc_nat).  [resolve(1134,a,1116,a)].
% 14.73/14.86  2405 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1134,a,1117,b)].
% 14.73/14.86  2406 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1134,a,1118,b)].
% 14.73/14.86  2407 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A).  [resolve(1571,b,1542,a)].
% 14.73/14.86  2408 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1571,b,1543,a)].
% 14.73/14.86  2409 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1571,b,1544,a)].
% 14.73/14.86  2410 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1571,b,1545,a)].
% 14.73/14.86  2411 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1571,b,1546,a)].
% 14.73/14.86  2412 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1571,b,1547,a)].
% 14.73/14.86  2413 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1571,b,1548,a)].
% 14.73/14.86  2414 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1571,b,1549,a)].
% 14.73/14.86  2415 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1571,b,1550,a)].
% 14.73/14.86  2416 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1571,b,1551,a)].
% 14.73/14.86  2417 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1571,b,1552,a)].
% 14.73/14.86  2418 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1596,a)].
% 14.73/14.86  2419 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1634,b,1597,a)].
% 14.73/14.86  2420 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1634,b,1598,a)].
% 14.81/14.95  2421 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1599,a)].
% 14.81/14.95  2422 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1634,b,1600,a)].
% 14.81/14.95  2423 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1634,b,1601,a)].
% 14.81/14.95  2424 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1634,b,1602,a)].
% 14.81/14.95  2425 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1634,b,1603,a)].
% 14.81/14.95  2426 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1634,b,1604,a)].
% 14.81/14.95  2427 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1634,b,1605,a)].
% 14.81/14.95  2428 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1634,b,1606,a)].
% 14.81/14.95  2429 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1634,b,1607,a)].
% 14.81/14.95  2430 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1634,b,1608,a)].
% 14.81/14.95  2431 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1634,b,1609,a)].
% 14.81/14.95  2432 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1634,b,1610,a)].
% 14.81/14.95  2433 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1634,b,1611,a)].
% 14.81/14.95  2434 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1634,b,1612,a)].
% 14.81/14.95  2435 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1634,b,1613,a)].
% 14.81/14.95  2436 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1634,b,1614,a)].
% 14.81/14.95  2437 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1634,b,1615,a)].
% 14.81/14.95  2438 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2020,b,2011,b)].
% 14.81/14.95  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2438,b,2387,b)].
% 14.81/14.95  2439 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2021,b,2011,b)].
% 14.81/14.95  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2439,b,2387,b)].
% 14.81/14.95  2440 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2022,b,2011,b)].
% 14.81/14.95  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2440,b,2387,b)].
% 14.81/14.95  2441 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2023,b,2011,b)].
% 14.81/14.95  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2441,b,2387,b)].
% 14.81/14.95  2442 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2024,b,2011,b)].
% 14.81/14.95  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2442,b,2387,b)].
% 14.81/14.95  2443 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2025,b,2011,b)].
% 14.81/14.95  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2443,b,2387,b)].
% 14.81/14.95  2444 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2026,c,2011,b)].
% 14.81/14.96  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2444,c,2387,b)].
% 14.81/14.96  2445 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A).  [resolve(2027,c,2011,b)].
% 14.81/14.96  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A).  [resolve(2445,c,2387,b)].
% 14.81/14.96  2446 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2032,a,2011,b)].
% 14.81/14.96  Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2446,b,2387,b)].
% 14.81/14.96  2447 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2033,a,2011,b)].
% 14.81/14.96  Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2447,c,2387,b)].
% 14.81/14.96  2448 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2034,a,2011,b)].
% 14.81/14.96  Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2448,b,2387,b)].
% 14.81/14.96  2449 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2035,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2449,c,2387,b)].
% 14.81/14.96  2450 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2036,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2450,c,2387,b)].
% 14.81/14.96  2451 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2037,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2451,c,2387,b)].
% 14.81/14.96  2452 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2038,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2452,c,2387,b)].
% 14.81/14.96  2453 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2039,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2453,c,2387,b)].
% 14.81/14.96  2454 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2040,a,2011,b)].
% 14.81/14.96  Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2454,c,2387,b)].
% 14.81/14.96  2455 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2041,a,2011,b)].
% 14.88/14.98  Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2455,b,2387,b)].
% 14.88/14.98  2456 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B).  [resolve(2042,a,2011,b)].
% 14.88/14.98  Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B).  [resolve(2456,b,2387,b)].
% 14.88/14.98  2457 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2043,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2457,c,2387,b)].
% 14.88/14.98  2458 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2044,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2458,c,2387,b)].
% 14.88/14.98  2459 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2045,a,2011,b)].
% 14.88/14.98  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2459,d,2387,b)].
% 14.88/14.98  2460 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2046,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2460,c,2387,b)].
% 14.88/14.98  2461 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2047,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2461,c,2387,b)].
% 14.88/14.98  2462 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2048,a,2011,b)].
% 14.88/14.98  Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2462,d,2387,b)].
% 14.88/14.98  2463 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2049,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2463,c,2387,b)].
% 14.88/14.98  2464 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2050,a,2011,b)].
% 14.88/14.98  Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2464,c,2387,b)].
% 14.88/14.98  2465 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2051,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2465,c,2387,b)].
% 14.88/14.98  2466 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2052,a,2011,b)].
% 14.88/14.98  Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2466,c,2387,b)].
% 14.88/14.98  2467 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2053,a,2011,b)].
% 14.88/14.98  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2467,c,2387,b)].
% 14.88/14.98  2468 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2054,a,2011,b)].
% 15.13/15.24  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2468,c,2387,b)].
% 15.13/15.24  2469 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2055,a,2011,b)].
% 15.13/15.24  Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2469,d,2387,b)].
% 15.13/15.24  2470 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2056,a,2011,b)].
% 15.13/15.24  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2470,c,2387,b)].
% 15.13/15.24  2471 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D).  [resolve(2057,a,2011,b)].
% 15.13/15.24  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D).  [resolve(2471,c,2387,b)].
% 15.13/15.24  2472 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2058,a,2011,b)].
% 15.13/15.24  Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2472,d,2387,b)].
% 15.13/15.24  2473 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2059,a,2011,b)].
% 15.13/15.24  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2473,c,2387,b)].
% 15.13/15.24  2474 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2060,a,2011,b)].
% 15.13/15.24  Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2474,c,2387,b)].
% 15.13/15.24  2475 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2061,a,2011,b)].
% 15.13/15.24  Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2475,c,2387,b)].
% 15.13/15.24  2476 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C).  [resolve(2062,a,2011,b)].
% 15.13/15.24  Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C).  [resolve(2476,c,2387,b)].
% 15.13/15.24  2477 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) # label(axiom).  [assumption].
% 15.13/15.24  2478 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom).  [assumption].
% 15.13/15.24  2479 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom).  [assumption].
% 15.13/15.24  2480 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) # label(axiom).  [assumption].
% 15.13/15.24  2481 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__field_36) # label(axiom).  [assumption].
% 15.13/15.24  2482 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__cancel__comm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_39) # label(axiom).  [assumption].
% 15.13/15.24  2483 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) # label(axiom).  [assumption].
% 15.13/15.24  2484 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) # label(axiom).  [assumption].
% 15.28/15.46  2485 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) # label(axiom).  [assumption].
% 15.28/15.46  2486 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) # label(axiom).  [assumption].
% 15.28/15.46  2487 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) # label(axiom).  [assumption].
% 15.28/15.46  2488 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(33,b,1,a)].
% 15.28/15.46  2489 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(33,b,3,a)].
% 15.28/15.46  2490 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(33,b,9,a)].
% 15.28/15.46  2491 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A).  [resolve(33,b,10,a)].
% 15.28/15.46  2492 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(154,b,131,b)].
% 15.28/15.46  2493 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(154,b,133,b)].
% 15.28/15.46  2494 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(165,a,154,b)].
% 15.28/15.46  2495 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(166,a,154,b)].
% 15.28/15.46  2496 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(199,b,193,b)].
% 15.28/15.46  2497 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(200,b,193,b)].
% 15.28/15.46  2498 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(236,a,224,b)].
% 15.28/15.46  2499 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(237,a,224,b)].
% 15.28/15.46  2500 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(241,a,224,b)].
% 15.28/15.46  2501 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(242,a,224,b)].
% 15.28/15.46  2502 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0.  [resolve(300,b,280,a)].
% 15.28/15.46  2503 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0.  [resolve(300,b,282,a)].
% 15.28/15.46  2504 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(314,a,300,b)].
% 15.28/15.46  2505 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(315,a,300,b)].
% 15.28/15.46  2506 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint).  [resolve(1132,a,1091,a)].
% 15.28/15.46  2507 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat).  [resolve(1132,a,1116,a)].
% 15.28/15.46  2508 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1132,a,1117,b)].
% 15.28/15.46  2509 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1132,a,1118,b)].
% 15.28/15.46  2510 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A).  [resolve(1568,b,1542,a)].
% 15.28/15.46  2511 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1568,b,1543,a)].
% 15.40/15.50  2512 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1568,b,1544,a)].
% 15.40/15.50  2513 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1568,b,1545,a)].
% 15.40/15.50  2514 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1568,b,1546,a)].
% 15.40/15.50  2515 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1568,b,1547,a)].
% 15.40/15.50  2516 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1568,b,1548,a)].
% 15.40/15.50  2517 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1568,b,1549,a)].
% 15.40/15.50  2518 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1568,b,1550,a)].
% 15.40/15.50  2519 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1568,b,1551,a)].
% 15.40/15.50  2520 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A).  [resolve(1568,b,1552,a)].
% 15.40/15.50  2521 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1596,a)].
% 15.40/15.50  2522 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1631,b,1597,a)].
% 15.40/15.50  2523 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1631,b,1598,a)].
% 15.40/15.50  2524 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1599,a)].
% 15.40/15.50  2525 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1631,b,1600,a)].
% 15.40/15.50  2526 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1631,b,1601,a)].
% 15.40/15.50  2527 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1631,b,1602,a)].
% 15.40/15.50  2528 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1631,b,1603,a)].
% 15.40/15.50  2529 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1631,b,1604,a)].
% 15.40/15.50  2530 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1631,b,1605,a)].
% 15.40/15.50  2531 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1631,b,1606,a)].
% 15.40/15.50  2532 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1631,b,1607,a)].
% 15.40/15.50  2533 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1631,b,1608,a)].
% 15.40/15.50  2534 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1631,b,1609,a)].
% 15.40/15.50  2535 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1631,b,1610,a)].
% 15.42/15.58  2536 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1631,b,1611,a)].
% 15.42/15.58  2537 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1631,b,1612,a)].
% 15.42/15.58  2538 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1631,b,1613,a)].
% 15.42/15.58  2539 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1631,b,1614,a)].
% 15.42/15.58  2540 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1631,b,1615,a)].
% 15.42/15.58  2541 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2022,b,2008,b)].
% 15.42/15.58  2542 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2023,b,2008,b)].
% 15.42/15.58  2543 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2024,b,2008,b)].
% 15.42/15.58  2544 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2025,b,2008,b)].
% 15.42/15.58  2545 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2026,c,2008,b)].
% 15.42/15.58  2546 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2027,c,2008,b)].
% 15.42/15.58  2547 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2032,a,2008,b)].
% 15.42/15.58  2548 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2033,a,2008,b)].
% 15.42/15.58  2549 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2034,a,2008,b)].
% 15.42/15.58  2550 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2035,a,2008,b)].
% 15.42/15.58  2551 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2036,a,2008,b)].
% 15.42/15.58  2552 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2037,a,2008,b)].
% 15.42/15.58  2553 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2038,a,2008,b)].
% 15.42/15.58  2554 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2039,a,2008,b)].
% 15.42/15.58  2555 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2040,a,2008,b)].
% 15.42/15.58  2556 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2041,a,2008,b)].
% 15.42/15.58  2557 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2042,a,2008,b)].
% 15.42/15.58  2558 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2043,a,2008,b)].
% 15.42/15.58  2559 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2044,a,2008,b)].
% 15.50/15.61  2560 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2045,a,2008,b)].
% 15.50/15.61  2561 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2046,a,2008,b)].
% 15.50/15.61  2562 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2047,a,2008,b)].
% 15.50/15.61  2563 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2048,a,2008,b)].
% 15.50/15.61  2564 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2049,a,2008,b)].
% 15.50/15.61  2565 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2050,a,2008,b)].
% 15.50/15.61  2566 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2051,a,2008,b)].
% 15.50/15.61  2567 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2052,a,2008,b)].
% 15.50/15.61  2568 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2053,a,2008,b)].
% 15.50/15.61  2569 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2054,a,2008,b)].
% 15.50/15.61  2570 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2055,a,2008,b)].
% 15.50/15.61  2571 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2056,a,2008,b)].
% 15.50/15.61  2572 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2057,a,2008,b)].
% 15.50/15.61  2573 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2058,a,2008,b)].
% 15.50/15.61  2574 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2059,a,2008,b)].
% 15.50/15.61  2575 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2060,a,2008,b)].
% 15.50/15.61  2576 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2061,a,2008,b)].
% 15.50/15.61  2577 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2062,a,2008,b)].
% 15.50/15.61  2578 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2090,a,2071,b)].
% 15.50/15.61  2579 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2091,a,2071,b)].
% 15.50/15.61  2580 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2092,c,2071,b)].
% 15.50/15.61  2581 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2093,c,2071,b)].
% 15.50/15.61  2582 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2094,b,2071,b)].
% 15.50/15.61  2583 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2095,a,2071,b)].
% 15.50/15.61  2584 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2131,b,2071,b)].
% 15.50/15.61  2585 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2132,b,2071,b)].
% 15.50/15.61  2586 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2133,b,2071,b)].
% 15.50/15.64  2587 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2134,b,2071,b)].
% 15.50/15.64  2588 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2135,c,2071,b)].
% 15.50/15.64  2589 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A).  [resolve(2136,c,2071,b)].
% 15.50/15.64  2590 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2137,b,2071,b)].
% 15.50/15.64  2591 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2138,c,2071,b)].
% 15.50/15.64  2592 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2139,b,2071,b)].
% 15.50/15.64  2593 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2140,c,2071,b)].
% 15.50/15.64  2594 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2141,c,2071,b)].
% 15.50/15.64  2595 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2142,c,2071,b)].
% 15.50/15.64  2596 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2143,c,2071,b)].
% 15.50/15.64  2597 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2144,c,2071,b)].
% 15.50/15.64  2598 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2145,c,2071,b)].
% 15.50/15.64  2599 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2146,b,2071,b)].
% 15.50/15.64  2600 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B).  [resolve(2147,b,2071,b)].
% 15.50/15.64  2601 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2148,c,2071,b)].
% 15.50/15.64  2602 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2149,c,2071,b)].
% 15.50/15.64  2603 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2150,d,2071,b)].
% 15.50/15.64  2604 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2151,c,2071,b)].
% 15.50/15.64  2605 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2152,c,2071,b)].
% 15.50/15.64  2606 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2153,d,2071,b)].
% 15.50/15.64  2607 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2154,c,2071,b)].
% 15.50/15.64  2608 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2155,c,2071,b)].
% 15.50/15.64  2609 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2156,c,2071,b)].
% 15.74/15.85  2610 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2157,c,2071,b)].
% 15.74/15.85  2611 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2158,c,2071,b)].
% 15.74/15.85  2612 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2159,c,2071,b)].
% 15.74/15.85  2613 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2160,d,2071,b)].
% 15.74/15.85  2614 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2161,c,2071,b)].
% 15.74/15.85  2615 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D).  [resolve(2162,c,2071,b)].
% 15.74/15.85  2616 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2163,d,2071,b)].
% 15.74/15.85  2617 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2164,c,2071,b)].
% 15.74/15.85  2618 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2165,c,2071,b)].
% 15.74/15.85  2619 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2166,c,2071,b)].
% 15.74/15.85  2620 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C).  [resolve(2167,c,2071,b)].
% 15.74/15.85  2621 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) # label(axiom).  [assumption].
% 15.74/15.85  2622 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom).  [assumption].
% 15.74/15.85  2623 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom).  [assumption].
% 15.74/15.85  2624 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) # label(axiom).  [assumption].
% 15.74/15.85  2625 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) # label(axiom).  [assumption].
% 15.74/15.85  2626 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) # label(axiom).  [assumption].
% 15.74/15.85  2627 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) # label(axiom).  [assumption].
% 15.74/15.85  2628 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) # label(axiom).  [assumption].
% 15.74/15.85  2629 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__field_35) # label(axiom).  [assumption].
% 15.74/15.85  2630 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oordered__comm__semiring__strict(A) # label(clsrel_Ring__and__Field_Oordered__idom_30) # label(axiom).  [assumption].
% 15.74/15.85  2631 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(27,b,1,a)].
% 15.74/15.85  2632 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(27,b,3,a)].
% 15.74/15.85  2633 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A).  [resolve(27,b,10,a)].
% 15.74/15.85  2634 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(81,b,65,b)].
% 15.74/15.91  2635 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(148,b,131,b)].
% 15.74/15.91  2636 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(148,b,133,b)].
% 15.74/15.91  2637 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(165,a,148,b)].
% 15.74/15.91  2638 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(166,a,148,b)].
% 15.74/15.91  2639 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(199,b,189,b)].
% 15.74/15.91  2640 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(200,b,189,b)].
% 15.74/15.91  2641 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(236,a,218,b)].
% 15.74/15.91  2642 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(237,a,218,b)].
% 15.74/15.91  2643 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(241,a,218,b)].
% 15.74/15.91  2644 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(242,a,218,b)].
% 15.74/15.91  2645 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0.  [resolve(294,b,280,a)].
% 15.74/15.91  2646 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0.  [resolve(294,b,282,a)].
% 15.74/15.91  2647 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(314,a,294,b)].
% 15.74/15.91  2648 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(315,a,294,b)].
% 15.74/15.91  2649 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(871,b,806,a)].
% 15.74/15.91  2650 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(871,b,807,a)].
% 15.74/15.91  2651 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(871,b,808,a)].
% 15.74/15.91  2652 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(871,b,809,a)].
% 15.74/15.91  2653 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,810,a)].
% 15.74/15.91  2654 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,811,a)].
% 15.74/15.91  2655 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(871,b,812,a)].
% 15.74/15.91  2656 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,813,a)].
% 15.74/15.91  2657 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(871,b,814,a)].
% 15.74/15.91  2658 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(871,b,815,a)].
% 15.74/15.91  2659 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(871,b,816,a)].
% 15.74/15.91  2660 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,817,a)].
% 15.74/15.91  2661 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,818,a)].
% 15.74/15.91  2662 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(871,b,819,a)].
% 15.74/15.91  2663 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,820,a)].
% 15.74/15.91  2664 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(871,b,821,a)].
% 15.74/15.91  2665 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(871,b,822,a)].
% 15.74/15.91  2666 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(871,b,823,a)].
% 15.74/15.91  2667 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(871,b,824,a)].
% 15.74/15.91  2668 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(871,b,825,a)].
% 15.74/15.91  2669 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(871,b,826,a)].
% 15.74/15.91  2670 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(871,b,827,a)].
% 15.74/15.91  2671 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(871,b,828,a)].
% 15.74/15.91  2672 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(871,b,829,b)].
% 15.74/15.91  2673 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(871,b,830,b)].
% 15.74/15.91  2674 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(871,b,831,a)].
% 15.74/15.91  2675 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(871,b,832,a)].
% 15.74/15.91  2676 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(871,b,833,a)].
% 15.82/15.92  2677 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(871,b,834,a)].
% 15.82/15.92  2678 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(871,b,835,a)].
% 15.82/15.92  2679 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(871,b,836,a)].
% 15.82/15.92  2680 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(871,b,837,a)].
% 15.82/15.92  2681 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(871,b,838,a)].
% 15.82/15.92  2682 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(871,b,839,a)].
% 15.82/15.92  2683 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(871,b,840,a)].
% 15.82/15.92  2684 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(871,b,841,a)].
% 15.82/15.92  2685 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(871,b,842,a)].
% 15.82/15.92  2686 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(871,b,843,a)].
% 15.82/15.92  2687 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(871,b,844,a)].
% 15.82/15.92  2688 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(871,b,845,a)].
% 15.82/15.92  2689 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(871,b,846,a)].
% 15.82/15.92  2690 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(871,b,847,a)].
% 15.82/15.92  2691 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(871,b,848,a)].
% 15.82/15.92  2692 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(871,b,849,a)].
% 15.82/15.92  2693 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(871,b,850,a)].
% 15.82/15.92  2694 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(871,b,851,a)].
% 15.82/15.92  2695 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(871,b,852,a)].
% 15.82/15.92  2696 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(871,b,853,a)].
% 15.82/15.92  2697 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(871,b,854,a)].
% 15.82/15.92  2698 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(871,b,855,a)].
% 15.82/15.92  2699 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(871,b,856,a)].
% 15.82/15.92  2700 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(871,b,857,a)].
% 15.98/16.07  2701 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(871,b,858,a)].
% 15.98/16.07  2702 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(871,b,859,a)].
% 15.98/16.07  2703 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(871,b,860,a)].
% 15.98/16.07  2704 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(871,b,861,a)].
% 15.98/16.07  2705 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(871,b,862,a)].
% 15.98/16.07  2706 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(871,b,863,a)].
% 15.98/16.07  2707 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1057,b,1046,a)].
% 15.98/16.07  2708 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1080,b,1069,a)].
% 15.98/16.07  2709 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint).  [resolve(1126,a,1091,a)].
% 15.98/16.07  2710 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).  [resolve(1126,a,1116,a)].
% 15.98/16.07  2711 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1126,a,1117,b)].
% 15.98/16.07  2712 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1126,a,1118,b)].
% 15.98/16.07  2713 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1459,b,1438,a)].
% 15.98/16.07  2714 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1459,b,1439,a)].
% 15.98/16.07  2715 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1459,b,1440,a)].
% 15.98/16.07  2716 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1459,b,1441,a)].
% 15.98/16.07  2717 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1459,b,1442,a)].
% 15.98/16.07  2718 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1459,b,1443,a)].
% 15.98/16.07  2719 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1459,b,1444,a)].
% 15.98/16.07  2720 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1459,b,1445,a)].
% 15.98/16.07  2721 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A).  [resolve(1564,b,1542,a)].
% 15.98/16.07  2722 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1564,b,1543,a)].
% 15.98/16.07  2723 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1564,b,1544,a)].
% 15.98/16.07  2724 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1564,b,1545,a)].
% 15.98/16.07  2725 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1564,b,1546,a)].
% 15.98/16.07  2726 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1564,b,1547,a)].
% 16.00/16.11  2727 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1564,b,1548,a)].
% 16.00/16.11  2728 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1564,b,1549,a)].
% 16.00/16.11  2729 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1564,b,1550,a)].
% 16.00/16.11  2730 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1564,b,1551,a)].
% 16.00/16.11  2731 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A).  [resolve(1564,b,1552,a)].
% 16.00/16.11  2732 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1596,a)].
% 16.00/16.11  2733 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1627,b,1597,a)].
% 16.00/16.11  2734 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1627,b,1598,a)].
% 16.00/16.11  2735 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1599,a)].
% 16.00/16.11  2736 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1627,b,1600,a)].
% 16.00/16.11  2737 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1627,b,1601,a)].
% 16.00/16.11  2738 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1627,b,1602,a)].
% 16.00/16.11  2739 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1627,b,1603,a)].
% 16.00/16.11  2740 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1627,b,1604,a)].
% 16.00/16.11  2741 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1627,b,1605,a)].
% 16.00/16.11  2742 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1627,b,1606,a)].
% 16.00/16.11  2743 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1627,b,1607,a)].
% 16.00/16.11  2744 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1627,b,1608,a)].
% 16.00/16.11  2745 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1627,b,1609,a)].
% 16.00/16.11  2746 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1627,b,1610,a)].
% 16.00/16.11  2747 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1627,b,1611,a)].
% 16.00/16.11  2748 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1627,b,1612,a)].
% 16.00/16.11  2749 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1627,b,1613,a)].
% 16.00/16.11  2750 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1627,b,1614,a)].
% 16.05/16.17  2751 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1627,b,1615,a)].
% 16.05/16.17  2752 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1802,a,1793,b)].
% 16.05/16.17  2753 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(1803,a,1793,b)].
% 16.05/16.17  2754 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1934,c,1854,b)].
% 16.05/16.17  2755 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1935,c,1854,b)].
% 16.05/16.17  2756 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1969,b,1854,b)].
% 16.05/16.17  2757 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1970,c,1854,b)].
% 16.05/16.17  2758 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1971,b,1854,b)].
% 16.05/16.17  2759 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1972,c,1854,b)].
% 16.05/16.17  2760 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1973,c,1854,b)].
% 16.05/16.17  2761 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1974,c,1854,b)].
% 16.05/16.17  2762 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1975,c,1854,b)].
% 16.05/16.17  2763 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1976,c,1854,b)].
% 16.05/16.17  2764 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1977,c,1854,b)].
% 16.05/16.17  2765 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1978,b,1854,b)].
% 16.05/16.17  2766 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(1979,b,1854,b)].
% 16.05/16.17  2767 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1980,c,1854,b)].
% 16.05/16.17  2768 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1981,c,1854,b)].
% 16.05/16.17  2769 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1982,d,1854,b)].
% 16.05/16.17  2770 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1983,c,1854,b)].
% 16.05/16.17  2771 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1984,c,1854,b)].
% 16.05/16.17  2772 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1985,d,1854,b)].
% 16.05/16.17  2773 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1986,c,1854,b)].
% 16.05/16.17  2774 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1987,c,1854,b)].
% 16.05/16.17  2775 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1988,c,1854,b)].
% 16.05/16.20  2776 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1989,c,1854,b)].
% 16.05/16.20  2777 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1990,c,1854,b)].
% 16.05/16.20  2778 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1991,c,1854,b)].
% 16.05/16.20  2779 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1992,d,1854,b)].
% 16.05/16.20  2780 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1993,c,1854,b)].
% 16.05/16.20  2781 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(1994,c,1854,b)].
% 16.05/16.20  2782 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1995,d,1854,b)].
% 16.05/16.20  2783 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1996,c,1854,b)].
% 16.05/16.20  2784 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1997,c,1854,b)].
% 16.05/16.20  2785 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1998,c,1854,b)].
% 16.05/16.20  2786 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(1999,c,1854,b)].
% 16.05/16.20  2787 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2022,b,2004,b)].
% 16.05/16.20  2788 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2023,b,2004,b)].
% 16.05/16.20  2789 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2024,b,2004,b)].
% 16.05/16.20  2790 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2025,b,2004,b)].
% 16.05/16.20  2791 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2026,c,2004,b)].
% 16.05/16.20  2792 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2027,c,2004,b)].
% 16.05/16.20  2793 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2090,a,2067,b)].
% 16.05/16.20  2794 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2091,a,2067,b)].
% 16.05/16.20  2795 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2131,b,2067,b)].
% 16.05/16.20  2796 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2132,b,2067,b)].
% 16.05/16.20  2797 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2133,b,2067,b)].
% 16.05/16.20  2798 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2134,b,2067,b)].
% 16.05/16.20  2799 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2135,c,2067,b)].
% 16.05/16.20  2800 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2136,c,2067,b)].
% 16.05/16.20  2801 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2137,b,2067,b)].
% 16.13/16.23  2802 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2138,c,2067,b)].
% 16.13/16.23  2803 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2139,b,2067,b)].
% 16.13/16.23  2804 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2140,c,2067,b)].
% 16.13/16.23  2805 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2141,c,2067,b)].
% 16.13/16.23  2806 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2142,c,2067,b)].
% 16.13/16.23  2807 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2143,c,2067,b)].
% 16.13/16.23  2808 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2144,c,2067,b)].
% 16.13/16.23  2809 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2145,c,2067,b)].
% 16.13/16.23  2810 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2146,b,2067,b)].
% 16.13/16.23  2811 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2147,b,2067,b)].
% 16.13/16.23  2812 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2148,c,2067,b)].
% 16.13/16.23  2813 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2149,c,2067,b)].
% 16.13/16.23  2814 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2150,d,2067,b)].
% 16.13/16.23  2815 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2151,c,2067,b)].
% 16.13/16.23  2816 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2152,c,2067,b)].
% 16.13/16.23  2817 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2153,d,2067,b)].
% 16.13/16.23  2818 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2154,c,2067,b)].
% 16.13/16.23  2819 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2155,c,2067,b)].
% 16.13/16.23  2820 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2156,c,2067,b)].
% 16.13/16.23  2821 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2157,c,2067,b)].
% 16.13/16.23  2822 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2158,c,2067,b)].
% 16.13/16.23  2823 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2159,c,2067,b)].
% 16.13/16.23  2824 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2160,d,2067,b)].
% 16.13/16.23  2825 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2161,c,2067,b)].
% 16.13/16.24  2826 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2162,c,2067,b)].
% 16.13/16.24  2827 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2163,d,2067,b)].
% 16.13/16.24  2828 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2164,c,2067,b)].
% 16.13/16.24  2829 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2165,c,2067,b)].
% 16.13/16.24  2830 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2166,c,2067,b)].
% 16.13/16.24  2831 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2167,c,2067,b)].
% 16.13/16.24  2832 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2197,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset.  [resolve(2832,e,2622,a)].
% 16.13/16.24  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset.  [resolve(2832,e,2623,a)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2832,e,2629,b)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2832,e,2630,b)].
% 16.13/16.24  2833 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2198,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2833,d,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(2833,d,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2833,d,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2833,d,2630,b)].
% 16.13/16.24  2834 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2199,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2834,d,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat).  [resolve(2834,d,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2834,d,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2834,d,2630,b)].
% 16.13/16.24  2835 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2200,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(2835,f,2622,a)].
% 16.13/16.24  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset.  [resolve(2835,f,2623,a)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2835,f,2629,b)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2835,f,2630,b)].
% 16.13/16.24  2836 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2201,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2836,e,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(2836,e,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2836,e,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2836,e,2630,b)].
% 16.13/16.24  2837 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2202,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2837,e,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(2837,e,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2837,e,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2837,e,2630,b)].
% 16.13/16.24  2838 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2203,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset.  [resolve(2838,f,2622,a)].
% 16.13/16.24  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset.  [resolve(2838,f,2623,a)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2838,f,2629,b)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2838,f,2630,b)].
% 16.13/16.24  2839 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2204,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2839,e,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(2839,e,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2839,e,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2839,e,2630,b)].
% 16.13/16.24  2840 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2205,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2840,e,2622,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset.  [resolve(2840,e,2623,a)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2840,e,2629,b)].
% 16.13/16.24  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2840,e,2630,b)].
% 16.13/16.24  2841 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2206,a,2171,b)].
% 16.13/16.24  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2841,b,2622,a)].
% 16.13/16.24  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(2841,b,2623,a)].
% 16.13/16.24  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2841,b,2629,b)].
% 16.13/16.24  Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2841,b,2630,b)].
% 16.13/16.24  2842 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2207,a,2171,b)].
% 16.13/16.24  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(2842,f,2622,a)].
% 16.13/16.24  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset.  [resolve(2842,f,2623,a)].
% 16.13/16.24  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2842,f,2629,b)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2842,f,2630,b)].
% 16.13/16.25  2843 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2208,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(2843,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(2843,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2843,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2843,e,2630,b)].
% 16.13/16.25  2844 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2209,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(2844,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(2844,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2844,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2844,e,2630,b)].
% 16.13/16.25  2845 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2210,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(2845,f,2622,a)].
% 16.13/16.25  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset.  [resolve(2845,f,2623,a)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2845,f,2629,b)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2845,f,2630,b)].
% 16.13/16.25  2846 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2211,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(2846,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(2846,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2846,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2846,e,2630,b)].
% 16.13/16.25  2847 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2212,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(2847,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(2847,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2847,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2847,e,2630,b)].
% 16.13/16.25  2848 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2213,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset.  [resolve(2848,d,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset.  [resolve(2848,d,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2848,d,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2848,d,2630,b)].
% 16.13/16.25  2849 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2214,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2849,d,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat).  [resolve(2849,d,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2849,d,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2849,d,2630,b)].
% 16.13/16.25  2850 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2215,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset.  [resolve(2850,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset.  [resolve(2850,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C).  [resolve(2850,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2850,e,2630,b)].
% 16.13/16.25  2851 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2216,a,2171,b)].
% 16.13/16.25  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2851,b,2622,a)].
% 16.13/16.25  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A.  [resolve(2851,b,2623,a)].
% 16.13/16.25  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2851,b,2629,b)].
% 16.13/16.25  Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2851,b,2630,b)].
% 16.13/16.25  2852 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2217,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset.  [resolve(2852,d,2622,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset.  [resolve(2852,d,2623,a)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B).  [resolve(2852,d,2629,b)].
% 16.13/16.25  Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2852,d,2630,b)].
% 16.13/16.25  2853 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2218,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2853,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A.  [resolve(2853,e,2623,a)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C).  [resolve(2853,e,2629,b)].
% 16.13/16.25  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2853,e,2630,b)].
% 16.13/16.25  2854 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2219,a,2171,b)].
% 16.13/16.25  Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A.  [resolve(2854,e,2622,a)].
% 16.13/16.25  Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A.  [resolve(2854,e,2623,a)].
% 16.13/16.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C).  [resolve(2854,e,2629,b)].
% 16.13/16.26  Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2854,e,2630,b)].
% 16.13/16.26  2855 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2220,a,2171,b)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint).  [resolve(2855,d,2622,a)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat).  [resolve(2855,d,2623,a)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2855,d,2629,b)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2855,d,2630,b)].
% 16.13/16.26  2856 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2221,a,2171,b)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(2856,d,2622,a)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat).  [resolve(2856,d,2623,a)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(2856,d,2629,b)].
% 16.13/16.26  Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(2856,d,2630,b)].
% 16.13/16.26  2857 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2222,a,2171,b)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2857,c,2622,a)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat).  [resolve(2857,c,2623,a)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2857,c,2629,b)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2857,c,2630,b)].
% 16.13/16.26  2858 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2223,a,2171,b)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(2858,c,2622,a)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat).  [resolve(2858,c,2623,a)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2858,c,2629,b)].
% 16.13/16.26  Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2858,c,2630,b)].
% 16.13/16.26  2859 -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2224,a,2171,b)].
% 16.13/16.26  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(2859,d,2622,a)].
% 16.13/16.26  Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(2859,d,2623,a)].
% 16.13/16.26  Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2859,d,2629,b)].
% 16.13/16.26  Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2859,d,2630,b)].
% 16.13/16.26  2860 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2225,a,2171,b)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(2860,c,2622,a)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2860,c,2623,a)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2860,c,2629,b)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2860,c,2630,b)].
% 16.13/16.26  2861 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2226,a,2171,b)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2861,c,2622,a)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2861,c,2623,a)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2861,c,2629,b)].
% 16.13/16.26  Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2861,c,2630,b)].
% 16.13/16.26  2862 -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2227,a,2171,b)].
% 16.13/16.26  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2862,d,2622,a)].
% 16.13/16.26  Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(2862,d,2623,a)].
% 16.13/16.26  Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2862,d,2629,b)].
% 16.13/16.26  Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2862,d,2630,b)].
% 16.13/16.26  2863 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2228,a,2171,b)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2863,c,2622,a)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2863,c,2623,a)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2863,c,2629,b)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2863,c,2630,b)].
% 16.13/16.26  2864 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2229,a,2171,b)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2864,c,2622,a)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2864,c,2623,a)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D).  [resolve(2864,c,2629,b)].
% 16.13/16.26  Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D).  [resolve(2864,c,2630,b)].
% 16.13/16.26  2865 -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2230,a,2171,b)].
% 16.13/16.26  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2865,d,2622,a)].
% 16.13/16.26  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat).  [resolve(2865,d,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2865,d,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2865,d,2630,b)].
% 16.13/16.27  2866 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2231,a,2171,b)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A.  [resolve(2866,b,2622,a)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,A,tc_nat) = A.  [resolve(2866,b,2623,a)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2866,b,2629,b)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2866,b,2630,b)].
% 16.13/16.27  2867 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2232,a,2171,b)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint).  [resolve(2867,b,2622,a)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat).  [resolve(2867,b,2623,a)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2867,b,2629,b)].
% 16.13/16.27  Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2867,b,2630,b)].
% 16.13/16.27  2868 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2233,a,2171,b)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2868,c,2622,a)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2868,c,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2868,c,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2868,c,2630,b)].
% 16.13/16.27  2869 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2234,a,2171,b)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(2869,c,2622,a)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(2869,c,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2869,c,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2869,c,2630,b)].
% 16.13/16.27  2870 -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2235,a,2171,b)].
% 16.13/16.27  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint).  [resolve(2870,d,2622,a)].
% 16.13/16.27  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat).  [resolve(2870,d,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2870,d,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2870,d,2630,b)].
% 16.13/16.27  2871 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2236,a,2171,b)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A.  [resolve(2871,b,2622,a)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,A,tc_nat) = A.  [resolve(2871,b,2623,a)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2871,b,2629,b)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2871,b,2630,b)].
% 16.13/16.27  2872 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2237,a,2171,b)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint).  [resolve(2872,b,2622,a)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat).  [resolve(2872,b,2623,a)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2872,b,2629,b)].
% 16.13/16.27  Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2872,b,2630,b)].
% 16.13/16.27  2873 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2238,a,2171,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint).  [resolve(2873,b,2622,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat).  [resolve(2873,b,2623,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2873,b,2629,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2873,b,2630,b)].
% 16.13/16.27  2874 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2239,a,2171,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint).  [resolve(2874,b,2622,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat).  [resolve(2874,b,2623,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2874,b,2629,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2874,b,2630,b)].
% 16.13/16.27  2875 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2240,a,2171,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint).  [resolve(2875,b,2622,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat).  [resolve(2875,b,2623,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2875,b,2629,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2875,b,2630,b)].
% 16.13/16.27  2876 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2241,a,2171,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint).  [resolve(2876,b,2622,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat).  [resolve(2876,b,2623,a)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2876,b,2629,b)].
% 16.13/16.27  Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2876,b,2630,b)].
% 16.13/16.27  2877 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2242,a,2171,b)].
% 16.13/16.27  Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B.  [resolve(2877,c,2622,a)].
% 16.13/16.27  Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B.  [resolve(2877,c,2623,a)].
% 16.13/16.27  Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(2877,c,2629,b)].
% 16.13/16.27  Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2877,c,2630,b)].
% 16.13/16.27  2878 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2243,a,2171,b)].
% 16.13/16.27  Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B.  [resolve(2878,c,2622,a)].
% 16.13/16.27  Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B.  [resolve(2878,c,2623,a)].
% 16.13/16.27  Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(2878,c,2629,b)].
% 16.13/16.27  Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2878,c,2630,b)].
% 16.13/16.27  2879 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2244,a,2171,b)].
% 16.13/16.27  Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B.  [resolve(2879,c,2622,a)].
% 16.13/16.27  Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B.  [resolve(2879,c,2623,a)].
% 16.13/16.27  Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(2879,c,2629,b)].
% 16.13/16.27  Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2879,c,2630,b)].
% 16.13/16.27  2880 -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2245,a,2171,b)].
% 16.13/16.27  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2880,c,2622,a)].
% 16.13/16.27  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(2880,c,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2880,c,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2880,c,2630,b)].
% 16.13/16.27  2881 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2246,a,2171,b)].
% 16.13/16.27  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2881,c,2622,a)].
% 16.13/16.27  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)).  [resolve(2881,c,2623,a)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2881,c,2629,b)].
% 16.13/16.27  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2881,c,2630,b)].
% 16.20/16.28  2882 -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2247,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint).  [resolve(2882,c,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat).  [resolve(2882,c,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2882,c,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2882,c,2630,b)].
% 16.20/16.28  2883 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2248,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2883,d,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2883,d,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2883,d,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2883,d,2630,b)].
% 16.20/16.28  2884 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2249,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2884,d,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2884,d,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2884,d,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2884,d,2630,b)].
% 16.20/16.28  2885 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2250,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2885,c,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)).  [resolve(2885,c,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2885,c,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2885,c,2630,b)].
% 16.20/16.28  2886 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2251,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2886,d,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)).  [resolve(2886,d,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2886,d,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2886,d,2630,b)].
% 16.20/16.28  2887 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2252,a,2171,b)].
% 16.20/16.28  Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B.  [resolve(2887,c,2622,a)].
% 16.20/16.28  Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B.  [resolve(2887,c,2623,a)].
% 16.20/16.28  Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B).  [resolve(2887,c,2629,b)].
% 16.20/16.28  Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2887,c,2630,b)].
% 16.20/16.28  2888 -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2253,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2888,c,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(2888,c,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B).  [resolve(2888,c,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2888,c,2630,b)].
% 16.20/16.28  2889 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2254,a,2171,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2889,c,2622,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)).  [resolve(2889,c,2623,a)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C).  [resolve(2889,c,2629,b)].
% 16.20/16.28  Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(2889,c,2630,b)].
% 16.20/16.29  2890 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2255,a,2171,b)].
% 16.20/16.29  Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A.  [resolve(2890,b,2622,a)].
% 16.20/16.29  Derived: c_LOrder_Ojoin(A,A,tc_nat) = A.  [resolve(2890,b,2623,a)].
% 16.20/16.29  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2890,b,2629,b)].
% 16.20/16.29  Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2890,b,2630,b)].
% 16.20/16.29  2891 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2256,a,2171,b)].
% 16.20/16.29  Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A.  [resolve(2891,b,2622,a)].
% 16.20/16.29  Derived: c_LOrder_Omeet(A,A,tc_nat) = A.  [resolve(2891,b,2623,a)].
% 16.20/16.29  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B).  [resolve(2891,b,2629,b)].
% 16.20/16.29  Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2891,b,2630,b)].
% 16.20/16.29  2892 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2261,a,2171,b)].
% 16.20/16.29  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(2892,c,2622,a)].
% 16.20/16.29  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat).  [resolve(2892,c,2623,a)].
% 16.20/16.29  2893 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2262,a,2171,b)].
% 16.20/16.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2893,c,2622,a)].
% 16.20/16.29  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(2893,c,2623,a)].
% 16.20/16.29  2894 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2263,a,2171,b)].
% 16.20/16.29  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2894,c,2622,a)].
% 16.20/16.29  Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2894,c,2623,a)].
% 16.20/16.29  2895 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2264,a,2171,b)].
% 16.20/16.29  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2895,c,2622,a)].
% 16.20/16.29  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(2895,c,2623,a)].
% 16.20/16.29  2896 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2265,a,2171,b)].
% 16.20/16.29  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(2896,c,2622,a)].
% 16.20/16.29  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat).  [resolve(2896,c,2623,a)].
% 16.20/16.29  2897 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2266,a,2171,b)].
% 16.20/16.29  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2897,c,2622,a)].
% 16.20/16.29  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat).  [resolve(2897,c,2623,a)].
% 16.20/16.29  2898 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2267,a,2171,b)].
% 16.20/16.29  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2898,c,2622,a)].
% 16.20/16.29  Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2898,c,2623,a)].
% 16.20/16.29  2899 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2268,a,2171,b)].
% 16.20/16.30  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2899,c,2622,a)].
% 16.20/16.30  Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat).  [resolve(2899,c,2623,a)].
% 16.20/16.30  2900 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2300,c,2171,b)].
% 16.20/16.30  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C.  [resolve(2900,c,2622,a)].
% 16.20/16.30  Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C.  [resolve(2900,c,2623,a)].
% 16.20/16.30  2901 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2301,c,2171,b)].
% 16.20/16.30  Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C.  [resolve(2901,c,2622,a)].
% 16.20/16.30  Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C.  [resolve(2901,c,2623,a)].
% 16.20/16.30  2902 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2302,b,2171,b)].
% 16.20/16.30  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(2902,b,2622,a)].
% 16.20/16.30  Derived: class_OrderedGroup_Osemigroup__add(tc_nat).  [resolve(2902,b,2623,a)].
% 16.20/16.30  2903 class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2303,b,2171,b)].
% 16.20/16.30  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(2903,b,2622,a)].
% 16.20/16.30  Derived: class_HOL_Oplus(tc_nat).  [resolve(2903,b,2623,a)].
% 16.20/16.30  2904 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2341,b,2171,b)].
% 16.20/16.30  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(2904,b,2622,a)].
% 16.20/16.30  Derived: c_times(c_0,A,tc_nat) = c_0.  [resolve(2904,b,2623,a)].
% 16.20/16.30  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(2904,b,2629,b)].
% 16.20/16.30  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2904,b,2630,b)].
% 16.20/16.30  2905 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2342,b,2171,b)].
% 16.20/16.30  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(2905,b,2622,a)].
% 16.20/16.30  Derived: c_times(A,c_0,tc_nat) = c_0.  [resolve(2905,b,2623,a)].
% 16.20/16.30  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(2905,b,2629,b)].
% 16.20/16.30  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(2905,b,2630,b)].
% 16.20/16.30  2906 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2343,b,2171,b)].
% 16.20/16.30  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(2906,b,2622,a)].
% 16.20/16.30  Derived: class_OrderedGroup_Osemigroup__mult(tc_nat).  [resolve(2906,b,2623,a)].
% 16.20/16.30  2907 class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2344,b,2171,b)].
% 16.20/16.30  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(2907,b,2622,a)].
% 16.20/16.30  Derived: class_HOL_Otimes(tc_nat).  [resolve(2907,b,2623,a)].
% 16.20/16.30  2908 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2345,b,2171,b)].
% 16.20/16.30  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(2908,b,2622,a)].
% 16.20/16.30  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat).  [resolve(2908,b,2623,a)].
% 16.20/16.30  2909 class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2346,b,2171,b)].
% 16.20/16.30  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(2909,b,2622,a)].
% 16.20/16.30  Derived: class_HOL_Ozero(tc_nat).  [resolve(2909,b,2623,a)].
% 16.20/16.30  2910 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2347,c,2171,b)].
% 16.20/16.30  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2910,c,2622,a)].
% 16.20/16.31  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat).  [resolve(2910,c,2623,a)].
% 16.20/16.31  2911 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A).  [resolve(2348,c,2171,b)].
% 16.20/16.31  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2911,c,2622,a)].
% 16.20/16.31  Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat).  [resolve(2911,c,2623,a)].
% 16.20/16.31  2912 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2349,b,2171,b)].
% 16.20/16.31  Derived: -c_less(A,A,tc_IntDef_Oint).  [resolve(2912,b,2622,a)].
% 16.20/16.31  Derived: -c_less(A,A,tc_nat).  [resolve(2912,b,2623,a)].
% 16.20/16.31  2913 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2350,c,2171,b)].
% 16.20/16.31  Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2913,c,2622,a)].
% 16.20/16.31  Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2913,c,2623,a)].
% 16.20/16.31  2914 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2351,b,2171,b)].
% 16.20/16.31  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2914,b,2622,a)].
% 16.20/16.31  Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat).  [resolve(2914,b,2623,a)].
% 16.20/16.31  2915 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2352,c,2171,b)].
% 16.20/16.31  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2915,c,2622,a)].
% 16.20/16.31  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset.  [resolve(2915,c,2623,a)].
% 16.20/16.31  2916 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2353,c,2171,b)].
% 16.20/16.31  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2916,c,2622,a)].
% 16.20/16.31  Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat).  [resolve(2916,c,2623,a)].
% 16.20/16.31  2917 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2354,c,2171,b)].
% 16.20/16.31  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2917,c,2622,a)].
% 16.20/16.31  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)).  [resolve(2917,c,2623,a)].
% 16.20/16.31  2918 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2355,c,2171,b)].
% 16.20/16.31  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2918,c,2622,a)].
% 16.20/16.32  Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat).  [resolve(2918,c,2623,a)].
% 16.20/16.32  2919 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2356,c,2171,b)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)).  [resolve(2919,c,2622,a)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)).  [resolve(2919,c,2623,a)].
% 16.20/16.32  2920 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2357,c,2171,b)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset.  [resolve(2920,c,2622,a)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset.  [resolve(2920,c,2623,a)].
% 16.20/16.32  2921 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2358,b,2171,b)].
% 16.20/16.32  Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint).  [resolve(2921,b,2622,a)].
% 16.20/16.32  Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat).  [resolve(2921,b,2623,a)].
% 16.20/16.32  2922 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B).  [resolve(2359,b,2171,b)].
% 16.20/16.32  Derived: c_lessequals(A,A,tc_IntDef_Oint).  [resolve(2922,b,2622,a)].
% 16.20/16.32  Derived: c_lessequals(A,A,tc_nat).  [resolve(2922,b,2623,a)].
% 16.20/16.32  2923 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2360,c,2171,b)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2923,c,2622,a)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2923,c,2623,a)].
% 16.20/16.32  2924 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2361,c,2171,b)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2924,c,2622,a)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2924,c,2623,a)].
% 16.20/16.32  2925 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2362,d,2171,b)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2925,d,2622,a)].
% 16.20/16.32  Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat).  [resolve(2925,d,2623,a)].
% 16.20/16.32  2926 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2363,c,2171,b)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2926,c,2622,a)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2926,c,2623,a)].
% 16.20/16.32  2927 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2364,c,2171,b)].
% 16.20/16.32  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2927,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2927,c,2623,a)].
% 16.20/16.33  2928 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2365,d,2171,b)].
% 16.20/16.33  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2928,d,2622,a)].
% 16.20/16.33  Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat).  [resolve(2928,d,2623,a)].
% 16.20/16.33  2929 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2366,c,2171,b)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint).  [resolve(2929,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(2929,c,2623,a)].
% 16.20/16.33  2930 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2367,c,2171,b)].
% 16.20/16.33  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2930,c,2622,a)].
% 16.20/16.33  Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat).  [resolve(2930,c,2623,a)].
% 16.20/16.33  2931 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2368,c,2171,b)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint).  [resolve(2931,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat).  [resolve(2931,c,2623,a)].
% 16.20/16.33  2932 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2369,c,2171,b)].
% 16.20/16.33  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2932,c,2622,a)].
% 16.20/16.33  Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat).  [resolve(2932,c,2623,a)].
% 16.20/16.33  2933 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2370,c,2171,b)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2933,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2933,c,2623,a)].
% 16.20/16.33  2934 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2371,c,2171,b)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(2934,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat).  [resolve(2934,c,2623,a)].
% 16.20/16.33  2935 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2372,d,2171,b)].
% 16.20/16.33  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2935,d,2622,a)].
% 16.20/16.33  Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat).  [resolve(2935,d,2623,a)].
% 16.20/16.33  2936 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2373,c,2171,b)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2936,c,2622,a)].
% 16.20/16.33  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2936,c,2623,a)].
% 16.20/16.33  2937 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D).  [resolve(2374,c,2171,b)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(2937,c,2622,a)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat).  [resolve(2937,c,2623,a)].
% 16.65/16.75  2938 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2375,d,2171,b)].
% 16.65/16.75  Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2938,d,2622,a)].
% 16.65/16.75  Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat).  [resolve(2938,d,2623,a)].
% 16.65/16.75  2939 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2376,c,2171,b)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint).  [resolve(2939,c,2622,a)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat).  [resolve(2939,c,2623,a)].
% 16.65/16.75  2940 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2377,c,2171,b)].
% 16.65/16.75  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2940,c,2622,a)].
% 16.65/16.75  Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat).  [resolve(2940,c,2623,a)].
% 16.65/16.75  2941 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2378,c,2171,b)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint).  [resolve(2941,c,2622,a)].
% 16.65/16.75  Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat).  [resolve(2941,c,2623,a)].
% 16.65/16.75  2942 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C).  [resolve(2379,c,2171,b)].
% 16.65/16.75  Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(2942,c,2622,a)].
% 16.65/16.75  Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat).  [resolve(2942,c,2623,a)].
% 16.65/16.75  2943 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_0) # label(axiom).  [assumption].
% 16.65/16.75  2944 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom).  [assumption].
% 16.65/16.75  2945 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_2) # label(axiom).  [assumption].
% 16.65/16.75  2946 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__field_42) # label(axiom).  [assumption].
% 16.65/16.75  2947 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__abs__if(A) # label(clsrel_Ring__and__Field_Oordered__idom_46) # label(axiom).  [assumption].
% 16.65/16.75  2948 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint).  [resolve(1287,a,1243,a)].
% 16.65/16.75  2949 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1287,a,1269,b)].
% 16.65/16.75  2950 class_Ring__and__Field_Oaxclass__abs__if(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1287,a,1270,b)].
% 16.65/16.75  2951 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1596,a)].
% 16.65/16.75  2952 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1625,b,1597,a)].
% 16.65/16.75  2953 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1625,b,1598,a)].
% 16.65/16.75  2954 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1599,a)].
% 16.97/17.07  2955 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1625,b,1600,a)].
% 16.97/17.07  2956 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1625,b,1601,a)].
% 16.97/17.07  2957 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1625,b,1602,a)].
% 16.97/17.07  2958 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1625,b,1603,a)].
% 16.97/17.07  2959 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1625,b,1604,a)].
% 16.97/17.07  2960 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1625,b,1605,a)].
% 16.97/17.07  2961 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1625,b,1606,a)].
% 16.97/17.07  2962 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1625,b,1607,a)].
% 16.97/17.07  2963 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1625,b,1608,a)].
% 16.97/17.07  2964 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1625,b,1609,a)].
% 16.97/17.07  2965 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1625,b,1610,a)].
% 16.97/17.07  2966 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1625,b,1611,a)].
% 16.97/17.07  2967 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1625,b,1612,a)].
% 16.97/17.07  2968 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1625,b,1613,a)].
% 16.97/17.07  2969 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1625,b,1614,a)].
% 16.97/17.07  2970 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1625,b,1615,a)].
% 16.97/17.07  2971 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom).  [assumption].
% 16.97/17.07  2972 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom).  [assumption].
% 16.97/17.07  2973 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Olordered__ring_0) # label(axiom).  [assumption].
% 16.97/17.07  2974 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_44) # label(axiom).  [assumption].
% 16.97/17.07  2975 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_49) # label(axiom).  [assumption].
% 16.97/17.07  2976 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom).  [assumption].
% 16.97/17.07  2977 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom).  [assumption].
% 16.97/17.07  2978 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Opordered__ring_13) # label(axiom).  [assumption].
% 16.97/17.07  2979 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Opordered__ring_14) # label(axiom).  [assumption].
% 16.97/17.07  2980 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_19) # label(axiom).  [assumption].
% 16.97/17.09  2981 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Opordered__ring_2) # label(axiom).  [assumption].
% 16.97/17.09  2982 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom).  [assumption].
% 16.97/17.09  2983 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Opordered__ring_9) # label(axiom).  [assumption].
% 16.97/17.09  2984 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(36,b,1,a)].
% 16.97/17.09  2985 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(36,b,3,a)].
% 16.97/17.09  2986 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(36,b,9,a)].
% 16.97/17.09  2987 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(36,b,10,a)].
% 16.97/17.09  2988 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(158,b,131,b)].
% 16.97/17.09  2989 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(158,b,133,b)].
% 16.97/17.09  2990 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(165,a,158,b)].
% 16.97/17.09  2991 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(166,a,158,b)].
% 16.97/17.09  2992 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(236,a,228,b)].
% 16.97/17.09  2993 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(237,a,228,b)].
% 16.97/17.09  2994 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(241,a,228,b)].
% 16.97/17.09  2995 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(242,a,228,b)].
% 16.97/17.09  2996 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(303,b,280,a)].
% 16.97/17.09  2997 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(303,b,282,a)].
% 16.97/17.09  2998 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(314,a,303,b)].
% 16.97/17.09  2999 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(315,a,303,b)].
% 16.97/17.09  3000 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(317,a,303,b)].
% 16.97/17.09  3001 class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(318,a,303,b)].
% 16.97/17.09  3002 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(338,b,321,b)].
% 16.97/17.09  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3002,a,2973,b)].
% 16.97/17.09  3003 -class_Ring__and__Field_Opordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(338,b,323,b)].
% 16.97/17.09  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3003,a,2973,b)].
% 16.97/17.09  3004 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(338,b,324,a)].
% 17.08/17.22  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3004,a,2973,b)].
% 17.08/17.22  3005 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(338,b,325,a)].
% 17.08/17.22  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3005,a,2973,b)].
% 17.08/17.22  3006 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(338,b,326,a)].
% 17.08/17.22  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3006,a,2973,b)].
% 17.08/17.22  3007 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(344,a,338,b)].
% 17.08/17.22  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3007,b,2973,b)].
% 17.08/17.22  3008 class_HOL_Ominus(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(345,a,338,b)].
% 17.08/17.22  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3008,b,2973,b)].
% 17.08/17.22  3009 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(356,b,338,b)].
% 17.08/17.22  3010 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(357,b,338,b)].
% 17.08/17.22  3011 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(358,b,338,b)].
% 17.08/17.22  3012 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(359,b,338,b)].
% 17.08/17.22  3013 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(360,c,338,b)].
% 17.08/17.22  3014 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(361,c,338,b)].
% 17.08/17.22  3015 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(362,a,338,b)].
% 17.08/17.22  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3015,b,2973,b)].
% 17.08/17.22  3016 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B).  [resolve(363,a,338,b)].
% 17.08/17.22  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3016,b,2973,b)].
% 17.08/17.22  3017 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(364,c,338,b)].
% 17.08/17.22  3018 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C).  [resolve(365,c,338,b)].
% 17.08/17.22  3019 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(788,a,708,a)].
% 17.08/17.22  3020 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(788,a,715,a)].
% 17.08/17.22  3021 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint).  [resolve(1291,a,1243,a)].
% 17.08/17.22  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3021,a,3002,a)].
% 17.08/17.22  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3021,a,3003,a)].
% 17.08/17.22  Derived: c_times(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(A,B,tc_IntDef_Oint).  [resolve(3021,a,3004,a)].
% 17.08/17.22  Derived: c_times(c_uminus(A,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3021,a,3005,a)].
% 17.08/17.22  Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3021,a,3006,a)].
% 17.08/17.22  3022 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1291,a,1269,b)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(3022,a,3002,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(3022,a,3003,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(3022,a,3004,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(3022,a,3005,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(3022,a,3006,a)].
% 17.18/17.25  3023 class_Ring__and__Field_Opordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1291,a,1270,b)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(3023,a,3002,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(3023,a,3003,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(3023,a,3004,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(3023,a,3005,a)].
% 17.18/17.25  Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(3023,a,3006,a)].
% 17.18/17.25  3024 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1463,b,1438,a)].
% 17.18/17.25  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3024,a,2973,b)].
% 17.18/17.25  3025 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1463,b,1439,a)].
% 17.18/17.25  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3025,a,2973,b)].
% 17.18/17.25  3026 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1463,b,1440,a)].
% 17.18/17.25  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3026,a,2973,b)].
% 17.18/17.25  3027 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1463,b,1441,a)].
% 17.18/17.25  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3027,a,2973,b)].
% 17.18/17.25  3028 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1463,b,1442,a)].
% 17.18/17.25  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3028,a,2973,b)].
% 17.18/17.25  3029 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1463,b,1443,a)].
% 17.18/17.25  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3029,a,2973,b)].
% 17.18/17.25  3030 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1463,b,1444,a)].
% 17.18/17.25  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3030,a,2973,b)].
% 17.18/17.25  3031 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1463,b,1445,a)].
% 17.22/17.32  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3031,a,2973,b)].
% 17.22/17.32  3032 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A).  [resolve(1572,b,1542,a)].
% 17.22/17.32  3033 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1572,b,1543,a)].
% 17.22/17.32  3034 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1572,b,1544,a)].
% 17.22/17.32  3035 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1572,b,1545,a)].
% 17.22/17.32  3036 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1572,b,1546,a)].
% 17.22/17.32  3037 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1572,b,1547,a)].
% 17.22/17.33  3038 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1572,b,1548,a)].
% 17.22/17.33  3039 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1572,b,1549,a)].
% 17.22/17.33  3040 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1572,b,1550,a)].
% 17.22/17.33  3041 -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1572,b,1551,a)].
% 17.22/17.33  3042 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A).  [resolve(1572,b,1552,a)].
% 17.22/17.33  3043 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1596,a)].
% 17.22/17.33  3044 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1635,b,1597,a)].
% 17.22/17.33  3045 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1635,b,1598,a)].
% 17.22/17.33  3046 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1599,a)].
% 17.22/17.33  3047 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1635,b,1600,a)].
% 17.22/17.33  3048 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1635,b,1601,a)].
% 17.22/17.33  3049 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1635,b,1602,a)].
% 17.22/17.33  3050 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1635,b,1603,a)].
% 17.22/17.33  3051 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1635,b,1604,a)].
% 17.22/17.33  3052 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1635,b,1605,a)].
% 17.22/17.33  3053 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1635,b,1606,a)].
% 17.22/17.33  3054 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1635,b,1607,a)].
% 17.22/17.33  3055 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1635,b,1608,a)].
% 17.22/17.33  3056 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1635,b,1609,a)].
% 17.22/17.33  3057 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1635,b,1610,a)].
% 17.28/17.38  3058 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1635,b,1611,a)].
% 17.28/17.38  3059 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1635,b,1612,a)].
% 17.28/17.38  3060 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1635,b,1613,a)].
% 17.28/17.38  3061 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1635,b,1614,a)].
% 17.28/17.38  3062 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1635,b,1615,a)].
% 17.28/17.38  3063 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(1748,b,1717,a)].
% 17.28/17.38  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3063,a,2973,b)].
% 17.28/17.38  3064 -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A).  [resolve(1748,b,1724,a)].
% 17.28/17.38  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3064,a,2973,b)].
% 17.28/17.38  3065 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2032,a,2012,b)].
% 17.28/17.38  3066 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2033,a,2012,b)].
% 17.28/17.38  3067 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2034,a,2012,b)].
% 17.28/17.38  3068 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2035,a,2012,b)].
% 17.28/17.38  3069 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2036,a,2012,b)].
% 17.28/17.38  3070 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2037,a,2012,b)].
% 17.28/17.38  3071 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2038,a,2012,b)].
% 17.28/17.38  3072 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2039,a,2012,b)].
% 17.28/17.38  3073 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2040,a,2012,b)].
% 17.28/17.38  3074 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2041,a,2012,b)].
% 17.28/17.38  3075 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B).  [resolve(2042,a,2012,b)].
% 17.28/17.38  3076 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2043,a,2012,b)].
% 17.28/17.38  3077 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2044,a,2012,b)].
% 17.28/17.38  3078 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2045,a,2012,b)].
% 17.28/17.38  3079 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2046,a,2012,b)].
% 17.28/17.38  3080 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2047,a,2012,b)].
% 17.28/17.38  3081 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2048,a,2012,b)].
% 17.28/17.38  3082 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2049,a,2012,b)].
% 17.28/17.38  3083 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2050,a,2012,b)].
% 17.28/17.38  3084 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2051,a,2012,b)].
% 17.55/17.64  3085 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2052,a,2012,b)].
% 17.55/17.64  3086 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2053,a,2012,b)].
% 17.55/17.64  3087 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2054,a,2012,b)].
% 17.55/17.64  3088 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2055,a,2012,b)].
% 17.55/17.64  3089 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2056,a,2012,b)].
% 17.55/17.64  3090 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D).  [resolve(2057,a,2012,b)].
% 17.55/17.64  3091 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2058,a,2012,b)].
% 17.55/17.64  3092 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2059,a,2012,b)].
% 17.55/17.64  3093 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2060,a,2012,b)].
% 17.55/17.64  3094 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2061,a,2012,b)].
% 17.55/17.64  3095 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C).  [resolve(2062,a,2012,b)].
% 17.55/17.64  3096 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2131,b,2077,b)].
% 17.55/17.64  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3096,b,2973,b)].
% 17.55/17.64  3097 class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2132,b,2077,b)].
% 17.55/17.64  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3097,b,2973,b)].
% 17.55/17.64  3098 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2133,b,2077,b)].
% 17.55/17.64  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3098,b,2973,b)].
% 17.55/17.64  3099 class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2134,b,2077,b)].
% 17.55/17.64  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3099,b,2973,b)].
% 17.55/17.64  3100 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2135,c,2077,b)].
% 17.55/17.64  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3100,c,2973,b)].
% 17.55/17.64  3101 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A).  [resolve(2136,c,2077,b)].
% 17.55/17.64  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3101,c,2973,b)].
% 17.55/17.64  3102 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_0) # label(axiom).  [assumption].
% 17.55/17.64  3103 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom).  [assumption].
% 17.55/17.64  3104 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom).  [assumption].
% 17.73/17.80  3105 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom).  [assumption].
% 17.73/17.80  3106 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_14) # label(axiom).  [assumption].
% 17.73/17.80  3107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_2) # label(axiom).  [assumption].
% 17.73/17.80  3108 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom).  [assumption].
% 17.73/17.80  3109 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_4) # label(axiom).  [assumption].
% 17.73/17.80  3110 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Olordered__ring_29) # label(axiom).  [assumption].
% 17.73/17.80  3111 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__field_48) # label(axiom).  [assumption].
% 17.73/17.80  3112 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__meet(A) # label(clsrel_Ring__and__Field_Oordered__idom_51) # label(axiom).  [assumption].
% 17.73/17.80  3113 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(14,b,1,a)].
% 17.73/17.80  3114 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(14,b,3,a)].
% 17.73/17.80  3115 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(81,b,52,b)].
% 17.73/17.80  3116 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(82,b,52,b)].
% 17.73/17.80  3117 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1054,b,1046,a)].
% 17.73/17.80  3118 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1077,b,1069,a)].
% 17.73/17.80  3119 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint).  [resolve(1293,a,1243,a)].
% 17.73/17.80  3120 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1293,a,1269,b)].
% 17.73/17.80  3121 class_OrderedGroup_Olordered__ab__group__meet(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1293,a,1270,b)].
% 17.73/17.80  3122 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1449,b,1438,a)].
% 17.73/17.80  3123 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1449,b,1439,a)].
% 17.73/17.80  3124 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1449,b,1440,a)].
% 17.73/17.80  3125 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1449,b,1441,a)].
% 17.73/17.80  3126 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1449,b,1442,a)].
% 17.73/17.80  3127 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1449,b,1443,a)].
% 17.73/17.80  3128 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1449,b,1444,a)].
% 17.73/17.80  3129 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1449,b,1445,a)].
% 17.73/17.80  3130 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1464,a,1449,b)].
% 17.73/17.80  3131 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1465,a,1449,b)].
% 17.73/17.80  3132 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1466,b,1449,b)].
% 17.73/17.80  3133 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A).  [resolve(1467,b,1449,b)].
% 17.73/17.81  3134 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1509,b,1476,a)].
% 17.73/17.81  Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint).  [resolve(3134,a,3103,a)].
% 17.73/17.81  3135 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1509,b,1477,a)].
% 17.73/17.81  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3135,a,3103,a)].
% 17.73/17.81  3136 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1509,b,1478,a)].
% 17.73/17.81  Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3136,a,3103,a)].
% 17.73/17.81  3137 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1509,b,1479,a)].
% 17.73/17.81  Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(3137,a,3103,a)].
% 17.73/17.81  3138 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1509,b,1480,a)].
% 17.73/17.81  Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3138,a,3103,a)].
% 17.73/17.81  3139 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1509,b,1481,a)].
% 17.73/17.81  Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0.  [resolve(3139,a,3103,a)].
% 17.73/17.81  3140 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1509,b,1482,a)].
% 17.73/17.81  Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3140,a,3103,a)].
% 17.73/17.81  3141 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1509,b,1483,a)].
% 17.73/17.81  Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3141,a,3103,a)].
% 17.73/17.81  3142 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1509,b,1484,a)].
% 17.73/17.81  Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(3142,a,3103,a)].
% 17.73/17.81  3143 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1509,b,1485,a)].
% 17.73/17.81  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0.  [resolve(3143,a,3103,a)].
% 17.73/17.81  3144 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1509,b,1486,a)].
% 17.73/17.81  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A.  [resolve(3144,a,3103,a)].
% 17.73/17.81  3145 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1509,b,1487,a)].
% 17.73/17.81  Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3145,a,3103,a)].
% 17.73/17.81  3146 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1509,b,1488,a)].
% 17.73/17.81  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3146,a,3103,a)].
% 17.73/17.81  3147 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1509,b,1489,a)].
% 17.73/17.81  Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0.  [resolve(3147,a,3103,a)].
% 17.73/17.81  3148 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1509,b,1490,a)].
% 17.73/17.81  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0.  [resolve(3148,a,3103,a)].
% 17.73/17.81  3149 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1509,b,1491,a)].
% 17.79/17.85  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A.  [resolve(3149,a,3103,a)].
% 17.79/17.85  3150 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1509,b,1492,a)].
% 17.79/17.85  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3150,a,3103,a)].
% 17.79/17.85  3151 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1509,b,1493,a)].
% 17.79/17.85  Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint).  [resolve(3151,a,3103,a)].
% 17.79/17.85  3152 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1509,b,1494,a)].
% 17.79/17.85  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3152,a,3103,a)].
% 17.79/17.85  3153 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1509,b,1495,a)].
% 17.79/17.85  Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3153,a,3103,a)].
% 17.79/17.85  3154 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1509,b,1496,a)].
% 17.79/17.85  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(3154,a,3103,a)].
% 17.79/17.85  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3154,a,3110,b)].
% 17.79/17.85  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3154,a,3111,b)].
% 17.79/17.85  Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3154,a,3112,b)].
% 17.79/17.85  3155 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1509,b,1497,a)].
% 17.79/17.85  Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint).  [resolve(3155,a,3103,a)].
% 17.79/17.85  3156 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A).  [resolve(1557,b,1542,a)].
% 17.79/17.85  3157 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1557,b,1543,a)].
% 17.79/17.85  3158 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1557,b,1544,a)].
% 17.79/17.85  3159 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1557,b,1545,a)].
% 17.79/17.85  3160 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1557,b,1546,a)].
% 17.79/17.85  3161 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1557,b,1547,a)].
% 17.79/17.85  3162 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1557,b,1548,a)].
% 17.79/17.85  3163 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1557,b,1549,a)].
% 17.79/17.85  3164 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1557,b,1550,a)].
% 17.79/17.85  3165 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1557,b,1551,a)].
% 17.79/17.85  3166 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A).  [resolve(1557,b,1552,a)].
% 17.79/17.85  3167 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1596,a)].
% 17.79/17.85  3168 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1620,b,1597,a)].
% 17.80/17.88  3169 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1620,b,1598,a)].
% 17.80/17.88  3170 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1599,a)].
% 17.80/17.88  3171 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1620,b,1600,a)].
% 17.80/17.88  3172 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1620,b,1601,a)].
% 17.80/17.88  3173 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1620,b,1602,a)].
% 17.80/17.88  3174 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1620,b,1603,a)].
% 17.80/17.88  3175 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1620,b,1604,a)].
% 17.80/17.88  3176 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1620,b,1605,a)].
% 17.80/17.88  3177 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1620,b,1606,a)].
% 17.80/17.88  3178 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1620,b,1607,a)].
% 17.80/17.88  3179 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1620,b,1608,a)].
% 17.80/17.88  3180 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1620,b,1609,a)].
% 17.80/17.88  3181 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1620,b,1610,a)].
% 17.80/17.88  3182 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1620,b,1611,a)].
% 17.80/17.88  3183 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1620,b,1612,a)].
% 17.80/17.88  3184 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1620,b,1613,a)].
% 17.80/17.88  3185 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1620,b,1614,a)].
% 17.80/17.88  3186 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1620,b,1615,a)].
% 17.80/17.88  3187 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1753,a,1721,b)].
% 17.80/17.88  3188 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1754,a,1721,b)].
% 17.80/17.88  3189 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1755,a,1721,b)].
% 17.80/17.88  3190 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1756,a,1721,b)].
% 17.80/17.88  3191 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1757,a,1721,b)].
% 17.80/17.88  3192 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1758,a,1721,b)].
% 17.80/17.88  3193 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1759,a,1721,b)].
% 17.80/17.88  3194 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1760,a,1721,b)].
% 18.10/18.17  3195 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1761,a,1721,b)].
% 18.10/18.17  3196 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1762,a,1721,b)].
% 18.10/18.17  3197 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B).  [resolve(1763,a,1721,b)].
% 18.10/18.17  3198 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1764,a,1721,b)].
% 18.10/18.17  3199 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1765,a,1721,b)].
% 18.10/18.17  3200 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1766,a,1721,b)].
% 18.10/18.17  3201 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1767,a,1721,b)].
% 18.10/18.17  3202 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1768,a,1721,b)].
% 18.10/18.17  3203 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1769,a,1721,b)].
% 18.10/18.17  3204 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1770,a,1721,b)].
% 18.10/18.17  3205 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1771,a,1721,b)].
% 18.10/18.17  3206 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1772,a,1721,b)].
% 18.10/18.17  3207 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1773,a,1721,b)].
% 18.10/18.17  3208 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1774,a,1721,b)].
% 18.10/18.17  3209 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1775,a,1721,b)].
% 18.10/18.17  3210 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1776,a,1721,b)].
% 18.10/18.17  3211 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1777,a,1721,b)].
% 18.10/18.17  3212 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D).  [resolve(1778,a,1721,b)].
% 18.10/18.17  3213 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1779,a,1721,b)].
% 18.10/18.17  3214 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1780,a,1721,b)].
% 18.10/18.17  3215 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1781,a,1721,b)].
% 18.10/18.17  3216 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1782,a,1721,b)].
% 18.10/18.17  3217 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C).  [resolve(1783,a,1721,b)].
% 18.10/18.17  3218 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_0) # label(axiom).  [assumption].
% 18.10/18.17  3219 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom).  [assumption].
% 18.10/18.17  3220 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom).  [assumption].
% 18.26/18.32  3221 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom).  [assumption].
% 18.26/18.32  3222 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_14) # label(axiom).  [assumption].
% 18.26/18.32  3223 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_2) # label(axiom).  [assumption].
% 18.26/18.32  3224 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom).  [assumption].
% 18.26/18.32  3225 -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_4) # label(axiom).  [assumption].
% 18.26/18.32  3226 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Olordered__ring_30) # label(axiom).  [assumption].
% 18.26/18.32  3227 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__field_49) # label(axiom).  [assumption].
% 18.26/18.32  3228 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group__join(A) # label(clsrel_Ring__and__Field_Oordered__idom_52) # label(axiom).  [assumption].
% 18.26/18.32  3229 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(13,b,1,a)].
% 18.26/18.32  3230 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(13,b,3,a)].
% 18.26/18.32  3231 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(81,b,51,b)].
% 18.26/18.32  3232 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(82,b,51,b)].
% 18.26/18.32  3233 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1053,b,1046,a)].
% 18.26/18.32  3234 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1076,b,1069,a)].
% 18.26/18.32  3235 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint).  [resolve(1294,a,1243,a)].
% 18.26/18.32  3236 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1294,a,1269,b)].
% 18.26/18.32  3237 class_OrderedGroup_Olordered__ab__group__join(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1294,a,1270,b)].
% 18.26/18.32  3238 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1448,b,1438,a)].
% 18.26/18.32  3239 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1448,b,1439,a)].
% 18.26/18.32  3240 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1448,b,1440,a)].
% 18.26/18.32  3241 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1448,b,1441,a)].
% 18.26/18.32  3242 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1448,b,1442,a)].
% 18.26/18.32  3243 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1448,b,1443,a)].
% 18.26/18.32  3244 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1448,b,1444,a)].
% 18.26/18.32  3245 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1448,b,1445,a)].
% 18.26/18.32  3246 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1464,a,1448,b)].
% 18.26/18.32  3247 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1465,a,1448,b)].
% 18.26/18.32  3248 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1466,b,1448,b)].
% 18.26/18.32  3249 class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A).  [resolve(1467,b,1448,b)].
% 18.26/18.35  3250 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1508,b,1476,a)].
% 18.26/18.35  3251 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1508,b,1477,a)].
% 18.26/18.35  3252 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1508,b,1478,a)].
% 18.26/18.35  3253 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1508,b,1479,a)].
% 18.26/18.35  3254 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1508,b,1480,a)].
% 18.26/18.35  3255 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1508,b,1481,a)].
% 18.26/18.35  3256 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1508,b,1482,a)].
% 18.26/18.35  3257 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1508,b,1483,a)].
% 18.26/18.35  3258 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1508,b,1484,a)].
% 18.26/18.35  3259 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1508,b,1485,a)].
% 18.26/18.35  3260 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1508,b,1486,a)].
% 18.26/18.35  3261 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1508,b,1487,a)].
% 18.26/18.35  3262 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1508,b,1488,a)].
% 18.26/18.35  3263 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1508,b,1489,a)].
% 18.26/18.35  3264 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1508,b,1490,a)].
% 18.26/18.35  3265 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1508,b,1491,a)].
% 18.26/18.35  3266 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1508,b,1492,a)].
% 18.26/18.35  3267 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1508,b,1493,a)].
% 18.26/18.35  3268 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1508,b,1494,a)].
% 18.26/18.35  3269 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1508,b,1495,a)].
% 18.26/18.35  3270 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1508,b,1496,a)].
% 18.26/18.35  3271 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A).  [resolve(1508,b,1497,a)].
% 18.26/18.35  3272 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A).  [resolve(1556,b,1542,a)].
% 18.26/18.35  3273 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1556,b,1543,a)].
% 18.26/18.35  3274 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1556,b,1544,a)].
% 18.26/18.35  3275 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1556,b,1545,a)].
% 18.26/18.35  3276 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1556,b,1546,a)].
% 18.26/18.35  3277 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1556,b,1547,a)].
% 18.33/18.40  3278 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1556,b,1548,a)].
% 18.33/18.40  3279 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1556,b,1549,a)].
% 18.33/18.40  3280 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1556,b,1550,a)].
% 18.33/18.40  3281 -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1556,b,1551,a)].
% 18.33/18.40  3282 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A).  [resolve(1556,b,1552,a)].
% 18.33/18.40  3283 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1596,a)].
% 18.33/18.40  3284 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1619,b,1597,a)].
% 18.33/18.40  3285 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1619,b,1598,a)].
% 18.33/18.40  3286 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1599,a)].
% 18.33/18.40  3287 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1619,b,1600,a)].
% 18.33/18.40  3288 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1619,b,1601,a)].
% 18.33/18.40  3289 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1619,b,1602,a)].
% 18.33/18.40  3290 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1619,b,1603,a)].
% 18.33/18.40  3291 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1619,b,1604,a)].
% 18.33/18.40  3292 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1619,b,1605,a)].
% 18.33/18.40  3293 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1619,b,1606,a)].
% 18.33/18.40  3294 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1619,b,1607,a)].
% 18.33/18.40  3295 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1619,b,1608,a)].
% 18.33/18.40  3296 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1619,b,1609,a)].
% 18.33/18.40  3297 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1619,b,1610,a)].
% 18.33/18.40  3298 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1619,b,1611,a)].
% 18.33/18.40  3299 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1619,b,1612,a)].
% 18.33/18.40  3300 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1619,b,1613,a)].
% 18.33/18.40  3301 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1619,b,1614,a)].
% 18.33/18.40  3302 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1619,b,1615,a)].
% 18.33/18.40  3303 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1753,a,1720,b)].
% 18.33/18.40  3304 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1754,a,1720,b)].
% 18.33/18.41  3305 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1755,a,1720,b)].
% 18.33/18.41  3306 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1756,a,1720,b)].
% 18.33/18.41  3307 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1757,a,1720,b)].
% 18.33/18.41  3308 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1758,a,1720,b)].
% 18.33/18.41  3309 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1759,a,1720,b)].
% 18.33/18.41  3310 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1760,a,1720,b)].
% 18.33/18.41  3311 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1761,a,1720,b)].
% 18.33/18.41  3312 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1762,a,1720,b)].
% 18.33/18.41  3313 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B).  [resolve(1763,a,1720,b)].
% 18.33/18.41  3314 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1764,a,1720,b)].
% 18.33/18.41  3315 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1765,a,1720,b)].
% 18.33/18.41  3316 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1766,a,1720,b)].
% 18.33/18.41  3317 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1767,a,1720,b)].
% 18.33/18.41  3318 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1768,a,1720,b)].
% 18.33/18.41  3319 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1769,a,1720,b)].
% 18.33/18.41  3320 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1770,a,1720,b)].
% 18.33/18.41  3321 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1771,a,1720,b)].
% 18.33/18.41  3322 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1772,a,1720,b)].
% 18.33/18.41  3323 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1773,a,1720,b)].
% 18.33/18.41  3324 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1774,a,1720,b)].
% 18.33/18.41  3325 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1775,a,1720,b)].
% 18.33/18.41  3326 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1776,a,1720,b)].
% 18.33/18.41  3327 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1777,a,1720,b)].
% 18.33/18.41  3328 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D).  [resolve(1778,a,1720,b)].
% 18.33/18.41  3329 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1779,a,1720,b)].
% 18.33/18.41  3330 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1780,a,1720,b)].
% 18.57/18.69  3331 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1781,a,1720,b)].
% 18.57/18.69  3332 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1782,a,1720,b)].
% 18.57/18.69  3333 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C).  [resolve(1783,a,1720,b)].
% 18.57/18.69  3334 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom).  [assumption].
% 18.57/18.69  3335 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom).  [assumption].
% 18.57/18.69  3336 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Olordered__ring_16) # label(axiom).  [assumption].
% 18.57/18.69  3337 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom).  [assumption].
% 18.57/18.69  3338 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Olordered__ring_18) # label(axiom).  [assumption].
% 18.57/18.69  3339 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_2) # label(axiom).  [assumption].
% 18.57/18.69  3340 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom).  [assumption].
% 18.57/18.69  3341 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Olordered__ring_23) # label(axiom).  [assumption].
% 18.57/18.69  3342 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom).  [assumption].
% 18.57/18.69  3343 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Olordered__ring_4) # label(axiom).  [assumption].
% 18.57/18.69  3344 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__field_43) # label(axiom).  [assumption].
% 18.57/18.69  3345 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Olordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__idom_48) # label(axiom).  [assumption].
% 18.57/18.69  3346 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(26,b,1,a)].
% 18.57/18.69  3347 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(26,b,3,a)].
% 18.57/18.69  3348 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(81,b,64,b)].
% 18.57/18.69  3349 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(82,b,64,b)].
% 18.57/18.69  3350 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(147,b,131,b)].
% 18.57/18.69  3351 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(147,b,133,b)].
% 18.57/18.69  3352 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(165,a,147,b)].
% 18.57/18.69  3353 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(166,a,147,b)].
% 18.57/18.69  3354 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(236,a,217,b)].
% 18.57/18.69  3355 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(237,a,217,b)].
% 18.57/18.69  3356 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(241,a,217,b)].
% 18.57/18.69  3357 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(242,a,217,b)].
% 18.72/18.82  3358 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0.  [resolve(293,b,280,a)].
% 18.72/18.82  3359 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0.  [resolve(293,b,282,a)].
% 18.72/18.82  3360 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(314,a,293,b)].
% 18.72/18.82  3361 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(315,a,293,b)].
% 18.72/18.82  3362 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(333,b,321,b)].
% 18.72/18.82  3363 -class_Ring__and__Field_Olordered__ring(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(333,b,323,b)].
% 18.72/18.82  3364 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(333,b,324,a)].
% 18.72/18.82  3365 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(333,b,325,a)].
% 18.72/18.82  3366 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(333,b,326,a)].
% 18.72/18.82  3367 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(344,a,333,b)].
% 18.72/18.82  3368 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(345,a,333,b)].
% 18.72/18.82  3369 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(352,b,333,b)].
% 18.72/18.82  3370 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(353,b,333,b)].
% 18.72/18.82  3371 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(356,b,333,b)].
% 18.72/18.82  3372 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(357,b,333,b)].
% 18.72/18.82  3373 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(358,b,333,b)].
% 18.72/18.82  3374 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(359,b,333,b)].
% 18.72/18.82  3375 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(360,c,333,b)].
% 18.72/18.82  3376 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(361,c,333,b)].
% 18.72/18.82  3377 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(362,a,333,b)].
% 18.72/18.82  3378 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(363,a,333,b)].
% 18.72/18.82  3379 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(364,c,333,b)].
% 18.72/18.82  3380 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(365,c,333,b)].
% 18.72/18.82  3381 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(783,a,708,a)].
% 18.72/18.82  3382 -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A).  [resolve(783,a,715,a)].
% 18.72/18.82  3383 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1056,b,1046,a)].
% 18.72/18.82  3384 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1079,b,1069,a)].
% 18.72/18.82  3385 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint).  [resolve(1290,a,1243,a)].
% 18.72/18.82  3386 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1290,a,1269,b)].
% 18.72/18.82  3387 class_Ring__and__Field_Olordered__ring(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1290,a,1270,b)].
% 18.72/18.82  3388 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0.  [resolve(1425,b,1396,a)].
% 18.72/18.83  Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0.  [resolve(3388,a,3335,a)].
% 18.72/18.83  3389 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A).  [resolve(1425,b,1397,a)].
% 18.72/18.83  Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint).  [resolve(3389,a,3335,a)].
% 18.72/18.83  3390 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).  [resolve(1425,b,1398,a)].
% 18.72/18.83  Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3390,a,3335,a)].
% 18.72/18.83  3391 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0.  [resolve(1425,b,1399,a)].
% 18.72/18.83  Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0.  [resolve(3391,a,3335,a)].
% 18.72/18.83  3392 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0.  [resolve(1425,b,1400,a)].
% 18.72/18.83  Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0.  [resolve(3392,a,3335,a)].
% 18.72/18.83  3393 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A).  [resolve(1425,b,1401,a)].
% 18.72/18.83  Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3393,a,3335,a)].
% 18.72/18.83  3394 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1425,b,1402,a)].
% 18.72/18.83  Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint).  [resolve(3394,a,3335,a)].
% 18.72/18.83  3395 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0.  [resolve(1425,b,1403,a)].
% 18.72/18.83  Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0.  [resolve(3395,a,3335,a)].
% 18.72/18.83  3396 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A).  [resolve(1425,b,1404,a)].
% 18.72/18.83  Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3396,a,3335,a)].
% 18.72/18.83  3397 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A).  [resolve(1425,b,1405,a)].
% 18.72/18.83  Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint).  [resolve(3397,a,3335,a)].
% 18.72/18.83  3398 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A).  [resolve(1425,b,1406,a)].
% 18.72/18.83  Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint).  [resolve(3398,a,3335,a)].
% 18.72/18.83  3399 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B.  [resolve(1425,b,1407,a)].
% 18.72/18.83  Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A.  [resolve(3399,a,3335,a)].
% 18.72/18.83  3400 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A).  [resolve(1425,b,1408,a)].
% 18.72/18.83  Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint).  [resolve(3400,a,3335,a)].
% 18.72/18.83  3401 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A).  [resolve(1425,b,1409,a)].
% 18.72/18.83  Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3401,a,3335,a)].
% 18.72/18.83  3402 -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0.  [resolve(1425,b,1410,a)].
% 18.72/18.83  Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0.  [resolve(3402,a,3335,a)].
% 18.72/18.83  3403 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A).  [resolve(1425,b,1412,a)].
% 18.72/18.83  3404 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A).  [resolve(1458,b,1438,a)].
% 18.72/18.83  3405 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1458,b,1439,a)].
% 18.72/18.83  3406 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A).  [resolve(1458,b,1440,a)].
% 18.72/18.83  3407 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1458,b,1441,a)].
% 18.72/18.86  3408 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A).  [resolve(1458,b,1442,a)].
% 18.72/18.86  3409 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A).  [resolve(1458,b,1443,a)].
% 18.72/18.86  3410 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A).  [resolve(1458,b,1444,a)].
% 18.72/18.86  3411 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A).  [resolve(1458,b,1445,a)].
% 18.72/18.86  3412 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A).  [resolve(1510,b,1476,a)].
% 18.72/18.86  3413 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A).  [resolve(1510,b,1477,a)].
% 18.72/18.86  3414 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1510,b,1478,a)].
% 18.72/18.86  3415 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1510,b,1479,a)].
% 18.72/18.86  3416 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0.  [resolve(1510,b,1480,a)].
% 18.72/18.86  3417 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0.  [resolve(1510,b,1481,a)].
% 18.72/18.86  3418 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1510,b,1482,a)].
% 18.72/18.86  3419 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A).  [resolve(1510,b,1483,a)].
% 18.72/18.86  3420 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0.  [resolve(1510,b,1484,a)].
% 18.72/18.86  3421 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0.  [resolve(1510,b,1485,a)].
% 18.72/18.86  3422 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B.  [resolve(1510,b,1486,a)].
% 18.72/18.86  3423 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A).  [resolve(1510,b,1487,a)].
% 18.72/18.86  3424 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A).  [resolve(1510,b,1488,a)].
% 18.72/18.86  3425 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0.  [resolve(1510,b,1489,a)].
% 18.72/18.86  3426 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0.  [resolve(1510,b,1490,a)].
% 18.72/18.86  3427 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B.  [resolve(1510,b,1491,a)].
% 18.72/18.86  3428 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A).  [resolve(1510,b,1492,a)].
% 18.72/18.86  3429 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A).  [resolve(1510,b,1493,a)].
% 18.72/18.86  3430 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A).  [resolve(1510,b,1494,a)].
% 18.72/18.86  3431 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A).  [resolve(1510,b,1495,a)].
% 18.72/18.86  3432 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(1537,c,1510,b)].
% 18.72/18.86  3433 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C).  [resolve(1538,c,1510,b)].
% 18.72/18.86  3434 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1539,b,1510,b)].
% 18.72/18.86  3435 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(1540,b,1510,b)].
% 18.72/18.86  3436 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A).  [resolve(1563,b,1542,a)].
% 18.72/18.86  3437 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1563,b,1543,a)].
% 18.72/18.86  3438 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1563,b,1544,a)].
% 18.81/18.88  3439 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1563,b,1545,a)].
% 18.81/18.88  3440 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1563,b,1546,a)].
% 18.81/18.88  3441 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1563,b,1547,a)].
% 18.81/18.88  3442 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1563,b,1548,a)].
% 18.81/18.88  3443 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1563,b,1549,a)].
% 18.81/18.88  3444 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1563,b,1550,a)].
% 18.81/18.88  3445 -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1563,b,1551,a)].
% 18.81/18.88  3446 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A).  [resolve(1563,b,1552,a)].
% 18.81/18.88  3447 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1596,a)].
% 18.81/18.88  3448 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1626,b,1597,a)].
% 18.81/18.88  3449 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1626,b,1598,a)].
% 18.81/18.88  3450 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1599,a)].
% 18.81/18.88  3451 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1626,b,1600,a)].
% 18.81/18.88  3452 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1626,b,1601,a)].
% 18.81/18.88  3453 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1626,b,1602,a)].
% 18.81/18.88  3454 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1626,b,1603,a)].
% 18.81/18.88  3455 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1626,b,1604,a)].
% 18.81/18.88  3456 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1626,b,1605,a)].
% 18.81/18.88  3457 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1626,b,1606,a)].
% 18.81/18.88  3458 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1626,b,1607,a)].
% 18.81/18.88  3459 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1626,b,1608,a)].
% 18.81/18.88  3460 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1626,b,1609,a)].
% 18.81/18.88  3461 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1626,b,1610,a)].
% 18.81/18.88  3462 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1626,b,1611,a)].
% 18.81/18.88  3463 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1626,b,1612,a)].
% 18.81/18.88  3464 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1626,b,1613,a)].
% 18.81/18.88  3465 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1626,b,1614,a)].
% 18.86/18.94  3466 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1626,b,1615,a)].
% 18.86/18.94  3467 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2032,a,2003,b)].
% 18.86/18.94  3468 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2033,a,2003,b)].
% 18.86/18.94  3469 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2034,a,2003,b)].
% 18.86/18.94  3470 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2035,a,2003,b)].
% 18.86/18.94  3471 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2036,a,2003,b)].
% 18.86/18.94  3472 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2037,a,2003,b)].
% 18.86/18.94  3473 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2038,a,2003,b)].
% 18.86/18.94  3474 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2039,a,2003,b)].
% 18.86/18.94  3475 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2040,a,2003,b)].
% 18.86/18.94  3476 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2041,a,2003,b)].
% 18.86/18.94  3477 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2042,a,2003,b)].
% 18.86/18.94  3478 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2043,a,2003,b)].
% 18.86/18.94  3479 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2044,a,2003,b)].
% 18.86/18.94  3480 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2045,a,2003,b)].
% 18.86/18.94  3481 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2046,a,2003,b)].
% 18.86/18.94  3482 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2047,a,2003,b)].
% 18.86/18.94  3483 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2048,a,2003,b)].
% 18.86/18.94  3484 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2049,a,2003,b)].
% 18.86/18.94  3485 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2050,a,2003,b)].
% 18.86/18.94  3486 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2051,a,2003,b)].
% 18.86/18.94  3487 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2052,a,2003,b)].
% 18.86/18.94  3488 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2053,a,2003,b)].
% 18.86/18.94  3489 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2054,a,2003,b)].
% 18.86/18.94  3490 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2055,a,2003,b)].
% 18.86/18.94  3491 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2056,a,2003,b)].
% 18.86/18.94  3492 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2057,a,2003,b)].
% 18.86/18.94  3493 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2058,a,2003,b)].
% 18.86/18.96  3494 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2059,a,2003,b)].
% 18.86/18.96  3495 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2060,a,2003,b)].
% 18.86/18.96  3496 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2061,a,2003,b)].
% 18.86/18.96  3497 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2062,a,2003,b)].
% 18.86/18.96  3498 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2131,b,2066,b)].
% 18.86/18.96  3499 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2132,b,2066,b)].
% 18.86/18.96  3500 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2133,b,2066,b)].
% 18.86/18.96  3501 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2134,b,2066,b)].
% 18.86/18.96  3502 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2135,c,2066,b)].
% 18.86/18.96  3503 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(2136,c,2066,b)].
% 18.86/18.96  3504 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2137,b,2066,b)].
% 18.86/18.96  3505 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2138,c,2066,b)].
% 18.86/18.96  3506 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2139,b,2066,b)].
% 18.86/18.96  3507 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2140,c,2066,b)].
% 18.86/18.96  3508 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2141,c,2066,b)].
% 18.86/18.96  3509 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2142,c,2066,b)].
% 18.86/18.96  3510 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2143,c,2066,b)].
% 18.86/18.96  3511 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2144,c,2066,b)].
% 18.86/18.96  3512 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2145,c,2066,b)].
% 18.86/18.96  3513 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2146,b,2066,b)].
% 18.86/18.96  3514 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(2147,b,2066,b)].
% 18.86/18.96  3515 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2148,c,2066,b)].
% 18.86/18.96  3516 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2149,c,2066,b)].
% 18.86/18.96  3517 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2150,d,2066,b)].
% 18.86/18.96  3518 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2151,c,2066,b)].
% 18.86/18.96  3519 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2152,c,2066,b)].
% 18.86/18.96  3520 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2153,d,2066,b)].
% 18.94/19.05  3521 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2154,c,2066,b)].
% 18.94/19.05  3522 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2155,c,2066,b)].
% 18.94/19.05  3523 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2156,c,2066,b)].
% 18.94/19.05  3524 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2157,c,2066,b)].
% 18.94/19.05  3525 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2158,c,2066,b)].
% 18.94/19.05  3526 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2159,c,2066,b)].
% 18.94/19.05  3527 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2160,d,2066,b)].
% 18.94/19.05  3528 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2161,c,2066,b)].
% 18.94/19.05  3529 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D).  [resolve(2162,c,2066,b)].
% 18.94/19.05  3530 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2163,d,2066,b)].
% 18.94/19.05  3531 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2164,c,2066,b)].
% 18.94/19.05  3532 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2165,c,2066,b)].
% 18.94/19.05  3533 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2166,c,2066,b)].
% 18.94/19.05  3534 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(2167,c,2066,b)].
% 18.94/19.05  3535 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3002,a,2973,b)].
% 18.94/19.05  3536 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3003,a,2973,b)].
% 18.94/19.05  3537 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3004,a,2973,b)].
% 18.94/19.05  3538 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3005,a,2973,b)].
% 18.94/19.05  3539 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3006,a,2973,b)].
% 18.94/19.05  3540 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3007,b,2973,b)].
% 18.94/19.05  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3540,b,3344,b)].
% 18.94/19.05  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3540,b,3345,b)].
% 18.94/19.05  3541 class_HOL_Ominus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3008,b,2973,b)].
% 18.94/19.05  Derived: class_HOL_Ominus(tc_IntDef_Oint).  [resolve(3541,b,3335,a)].
% 18.94/19.05  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3541,b,3344,b)].
% 18.94/19.05  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3541,b,3345,b)].
% 18.94/19.05  3542 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3015,b,2973,b)].
% 18.94/19.05  Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0.  [resolve(3542,b,3335,a)].
% 18.94/19.05  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(3542,b,3344,b)].
% 18.94/19.05  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(3542,b,3345,b)].
% 18.94/19.06  3543 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B).  [resolve(3016,b,2973,b)].
% 18.94/19.06  Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0.  [resolve(3543,b,3335,a)].
% 18.94/19.06  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B).  [resolve(3543,b,3344,b)].
% 18.94/19.06  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B).  [resolve(3543,b,3345,b)].
% 18.94/19.06  3544 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3024,a,2973,b)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint).  [resolve(3544,c,3335,a)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3544,c,3344,b)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3544,c,3345,b)].
% 18.94/19.06  3545 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3025,a,2973,b)].
% 18.94/19.06  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3545,c,3335,a)].
% 18.94/19.06  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3545,c,3344,b)].
% 18.94/19.06  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3545,c,3345,b)].
% 18.94/19.06  3546 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3026,a,2973,b)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint).  [resolve(3546,c,3335,a)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3546,c,3344,b)].
% 18.94/19.06  Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3546,c,3345,b)].
% 18.94/19.06  3547 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3027,a,2973,b)].
% 18.94/19.06  Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3547,c,3335,a)].
% 18.94/19.06  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3547,c,3344,b)].
% 18.94/19.06  Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3547,c,3345,b)].
% 18.94/19.06  3548 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3028,a,2973,b)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint).  [resolve(3548,c,3335,a)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3548,c,3344,b)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3548,c,3345,b)].
% 18.94/19.06  3549 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3029,a,2973,b)].
% 18.94/19.06  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3549,c,3335,a)].
% 18.94/19.06  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3549,c,3344,b)].
% 18.94/19.06  Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3549,c,3345,b)].
% 18.94/19.06  3550 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3030,a,2973,b)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint).  [resolve(3550,c,3335,a)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3550,c,3344,b)].
% 18.94/19.06  Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3550,c,3345,b)].
% 18.94/19.06  3551 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C).  [resolve(3031,a,2973,b)].
% 18.94/19.06  Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3551,c,3335,a)].
% 18.94/19.06  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C).  [resolve(3551,c,3344,b)].
% 18.94/19.06  Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C).  [resolve(3551,c,3345,b)].
% 18.94/19.06  3552 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3063,a,2973,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint).  [resolve(3552,b,3335,a)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3552,b,3344,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3552,b,3345,b)].
% 18.94/19.06  3553 class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3064,a,2973,b)].
% 18.94/19.06  Derived: class_HOL_Oplus(tc_IntDef_Oint).  [resolve(3553,b,3335,a)].
% 18.94/19.06  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3553,b,3344,b)].
% 18.94/19.06  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3553,b,3345,b)].
% 18.94/19.06  3554 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3096,b,2973,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint).  [resolve(3554,b,3335,a)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3554,b,3344,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3554,b,3345,b)].
% 18.94/19.06  3555 class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3097,b,2973,b)].
% 18.94/19.06  Derived: class_HOL_Otimes(tc_IntDef_Oint).  [resolve(3555,b,3335,a)].
% 18.94/19.06  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3555,b,3344,b)].
% 18.94/19.06  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3555,b,3345,b)].
% 18.94/19.06  3556 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3098,b,2973,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint).  [resolve(3556,b,3335,a)].
% 18.94/19.06  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3556,b,3344,b)].
% 18.94/19.06  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3556,b,3345,b)].
% 18.94/19.06  3557 class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3099,b,2973,b)].
% 18.94/19.06  Derived: class_HOL_Ozero(tc_IntDef_Oint).  [resolve(3557,b,3335,a)].
% 18.94/19.06  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3557,b,3344,b)].
% 18.94/19.06  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3557,b,3345,b)].
% 18.94/19.06  3558 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3100,c,2973,b)].
% 18.94/19.06  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3558,c,3335,a)].
% 18.94/19.06  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3558,c,3344,b)].
% 19.55/19.62  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3558,c,3345,b)].
% 19.55/19.62  3559 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3101,c,2973,b)].
% 19.55/19.62  Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint).  [resolve(3559,c,3335,a)].
% 19.55/19.62  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(3559,c,3344,b)].
% 19.55/19.62  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(3559,c,3345,b)].
% 19.55/19.62  3560 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A).  [resolve(3154,a,3110,b)].
% 19.55/19.62  Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint).  [resolve(3560,b,3335,a)].
% 19.55/19.62  3561 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) # label(axiom).  [assumption].
% 19.55/19.62  3562 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_54) # label(axiom).  [assumption].
% 19.55/19.62  3563 -class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) # label(axiom).  [assumption].
% 19.55/19.62  3564 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Ofield_32) # label(axiom).  [assumption].
% 19.55/19.62  3565 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oidom_30) # label(axiom).  [assumption].
% 19.55/19.62  3566 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__field_31) # label(axiom).  [assumption].
% 19.55/19.62  3567 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__no__zero__divisors(A) # label(clsrel_Ring__and__Field_Oordered__idom_56) # label(axiom).  [assumption].
% 19.55/19.62  3568 class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint).  [resolve(1295,a,1243,a)].
% 19.55/19.62  3569 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__field(A).  [resolve(1295,a,1269,b)].
% 19.55/19.62  3570 class_Ring__and__Field_Oaxclass__no__zero__divisors(A) | -class_Ring__and__Field_Oordered__idom(A).  [resolve(1295,a,1270,b)].
% 19.55/19.62  3571 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom).  [assumption].
% 19.55/19.62  3572 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom).  [assumption].
% 19.55/19.62  3573 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom).  [assumption].
% 19.55/19.62  Derived: class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3571,a,3573,b)].
% 19.55/19.62  3574 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom).  [assumption].
% 19.55/19.62  3575 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom).  [assumption].
% 19.55/19.62  3576 -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oidom_22) # label(axiom).  [assumption].
% 19.55/19.64  3577 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom).  [assumption].
% 19.55/19.64  3578 -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oidom_24) # label(axiom).  [assumption].
% 19.55/19.64  3579 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom).  [assumption].
% 19.55/19.64  3580 -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oidom_29) # label(axiom).  [assumption].
% 19.55/19.64  3581 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom).  [assumption].
% 19.55/19.64  3582 -class_Ring__and__Field_Oidom(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Oidom_5) # label(axiom).  [assumption].
% 19.55/19.64  3583 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom).  [assumption].
% 19.55/19.64  Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3583,a,3573,b)].
% 19.55/19.64  3584 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom).  [assumption].
% 19.55/19.64  3585 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom).  [assumption].
% 19.55/19.64  Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__ring__1(A).  [resolve(3585,b,3571,a)].
% 19.55/19.64  3586 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D.  [resolve(25,b,1,a)].
% 19.55/19.64  3587 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D.  [resolve(25,b,3,a)].
% 19.55/19.64  3588 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(81,b,63,b)].
% 19.55/19.64  3589 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(82,b,63,b)].
% 19.55/19.64  3590 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B.  [resolve(124,b,108,a)].
% 19.55/19.64  3591 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B.  [resolve(124,b,111,a)].
% 19.55/19.64  3592 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(146,b,131,b)].
% 19.55/19.64  3593 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(146,b,133,b)].
% 19.55/19.64  3594 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(165,a,146,b)].
% 19.55/19.64  3595 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(166,a,146,b)].
% 19.55/19.64  3596 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(199,b,188,b)].
% 19.55/19.64  3597 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(200,b,188,b)].
% 19.55/19.64  3598 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(236,a,216,b)].
% 19.55/19.64  3599 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(237,a,216,b)].
% 19.55/19.64  3600 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(241,a,216,b)].
% 19.55/19.64  3601 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(242,a,216,b)].
% 19.55/19.64  3602 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0.  [resolve(292,b,280,a)].
% 19.55/19.64  3603 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0.  [resolve(292,b,282,a)].
% 19.55/19.64  3604 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(314,a,292,b)].
% 19.55/19.64  3605 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(315,a,292,b)].
% 19.55/19.66  3606 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A).  [resolve(332,b,321,b)].
% 19.55/19.66  3607 -class_Ring__and__Field_Oidom(A) | -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A).  [resolve(332,b,323,b)].
% 19.55/19.66  3608 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),c_uminus(C,A),A) = c_times(B,C,A).  [resolve(332,b,324,a)].
% 19.55/19.66  3609 -class_Ring__and__Field_Oidom(A) | c_times(c_uminus(B,A),C,A) = c_uminus(c_times(B,C,A),A).  [resolve(332,b,325,a)].
% 19.55/19.66  3610 -class_Ring__and__Field_Oidom(A) | c_times(B,c_uminus(C,A),A) = c_uminus(c_times(B,C,A),A).  [resolve(332,b,326,a)].
% 19.55/19.66  3611 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(344,a,332,b)].
% 19.55/19.66  Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3611,b,3573,b)].
% 19.55/19.66  3612 class_HOL_Ominus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(345,a,332,b)].
% 19.55/19.66  Derived: class_HOL_Ominus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3612,b,3573,b)].
% 19.55/19.66  3613 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A).  [resolve(356,b,332,b)].
% 19.55/19.66  Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3613,b,3573,b)].
% 19.55/19.66  3614 class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A).  [resolve(357,b,332,b)].
% 19.55/19.66  Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3614,b,3573,b)].
% 19.55/19.66  3615 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(358,b,332,b)].
% 19.55/19.66  Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3615,b,3573,b)].
% 19.55/19.66  3616 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(359,b,332,b)].
% 19.55/19.66  3617 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(360,c,332,b)].
% 19.55/19.66  Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(3617,c,3573,b)].
% 19.55/19.66  3618 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(361,c,332,b)].
% 19.55/19.66  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(3618,c,3573,b)].
% 19.55/19.66  3619 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(362,a,332,b)].
% 19.55/19.66  3620 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(363,a,332,b)].
% 19.55/19.66  3621 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C).  [resolve(364,c,332,b)].
% 19.55/19.66  Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C).  [resolve(3621,c,3573,b)].
% 19.55/19.66  3622 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C).  [resolve(365,c,332,b)].
% 19.55/19.66  Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C).  [resolve(3622,c,3573,b)].
% 19.55/19.66  3623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A).  [resolve(463,b,421,b)].
% 19.55/19.66  3624 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(464,b,421,b)].
% 19.55/19.66  3625 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(501,a,495,b)].
% 19.55/19.66  3626 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(508,a,495,b)].
% 19.55/19.66  3627 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(509,a,495,b)].
% 19.55/19.66  3628 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(551,b,531,b)].
% 19.55/19.66  3629 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(552,b,531,b)].
% 19.55/19.67  3630 -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(630,a,596,b)].
% 19.55/19.67  Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(3630,c,3573,b)].
% 19.55/19.67  3631 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A).  [resolve(631,a,596,b)].
% 19.55/19.67  Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A).  [resolve(3631,c,3573,b)].
% 19.55/19.67  3632 c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Oidom(B).  [resolve(632,a,596,b)].
% 19.55/19.67  Derived: c_times(c_uminus(A,B),c_uminus(C,B),B) = c_times(A,C,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3632,b,3573,b)].
% 19.55/19.67  3633 c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B).  [resolve(633,a,596,b)].
% 19.55/19.67  Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B).  [resolve(3633,b,3573,b)].
% 19.55/19.67  3634 c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Oidom(C).  [resolve(634,a,596,b)].
% 19.55/19.67  Derived: c_times(A,c_uminus(B,C),C) = c_uminus(c_times(A,B,C),C) | -class_Ring__and__Field_Ofield(C).  [resolve(3634,b,3573,b)].
% 19.55/19.67  3635 class_HOL_Oone(A) | -class_Ring__and__Field_Oidom(A).  [resolve(635,b,596,b)].
% 19.55/19.67  Derived: class_HOL_Oone(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3635,b,3573,b)].
% 19.55/19.67  3636 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(636,b,596,b)].
% 19.55/19.67  Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(3636,b,3573,b)].
% 19.55/19.67  3637 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B).  [resolve(637,b,596,b)].
% 19.55/19.67  Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B).  [resolve(3637,b,3573,b)].
% 19.55/19.67  3638 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(639,b,596,b)].
% 19.55/19.67  Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(3638,b,3573,b)].
% 19.55/19.67  3639 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B).  [resolve(640,b,596,b)].
% 19.55/19.67  Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B).  [resolve(3639,b,3573,b)].
% 19.55/19.67  3640 class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A).  [resolve(642,b,596,b)].
% 19.55/19.67  Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3640,b,3573,b)].
% 19.55/19.67  3641 class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A).  [resolve(643,b,596,b)].
% 19.55/19.67  Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3641,b,3573,b)].
% 19.55/19.67  3642 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A).  [resolve(670,b,644,a)].
% 19.55/19.67  Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3642,a,3573,b)].
% 19.55/19.67  3643 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A).  [resolve(670,b,646,a)].
% 19.55/19.67  Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3643,a,3573,b)].
% 19.55/19.67  3644 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A).  [resolve(670,b,647,a)].
% 19.55/19.67  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3644,a,3573,b)].
% 19.55/19.67  3645 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A).  [resolve(670,b,648,a)].
% 19.55/19.67  Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3645,a,3573,b)].
% 21.44/21.52  3646 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A).  [resolve(670,b,649,a)].
% 21.44/21.52  Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3646,a,3573,b)].
% 21.44/21.52  3647 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A).  [resolve(670,b,650,a)].
% 21.44/21.52  Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Ofield(B).  [resolve(3647,a,3573,b)].
% 21.44/21.52  3648 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1.  [resolve(670,b,651,a)].
% 21.44/21.52  Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A).  [resolve(3648,a,3573,b)].
% 21.44/21.52  3649 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(670,b,652,a)].
% 21.44/21.52  Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C).  [resolve(3649,a,3573,b)].
% 21.44/21.52  3650 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A).  [resolve(670,b,653,a)].
% 21.44/21.52  Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C).  [resolve(3650,a,3573,b)].
% 21.44/21.52  3651 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A).  [resolve(670,b,654,a)].
% 21.44/21.52  Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A).  [resolve(3651,a,3573,b)].
% 21.44/21.52  3652 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A).  [resolve(800,a,708,a)].
% 21.44/21.52  Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A).  [resolve(3652,a,3573,b)].
% 21.44/21.52  3653 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset.  [resolve(877,b,806,a)].
% 21.44/21.52  3654 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom).  [assumption].
% 21.44/21.52  3655 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset.  [resolve(877,b,807,a)].
% 21.44/21.52  3656 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A).  [resolve(877,b,808,a)].
% 21.44/21.52  3657 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset.  [resolve(877,b,809,a)].
% 21.44/21.52  3658 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,810,a)].
% 21.44/21.52  3659 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,811,a)].
% 21.44/21.52  3660 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset.  [resolve(877,b,812,a)].
% 21.44/21.52  3661 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,813,a)].
% 21.44/21.52  3662 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset.  [resolve(877,b,814,a)].
% 21.44/21.52  3663 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,815,a)].
% 21.44/21.52  3664 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset.  [resolve(877,b,816,a)].
% 21.44/21.53  3665 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,817,a)].
% 21.44/21.53  3666 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,818,a)].
% 21.44/21.53  3667 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset.  [resolve(877,b,819,a)].
% 21.44/21.53  3668 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,820,a)].
% 21.44/21.53  3669 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset.  [resolve(877,b,821,a)].
% 21.44/21.53  3670 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset.  [resolve(877,b,822,a)].
% 21.44/21.53  3671 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A).  [resolve(877,b,823,a)].
% 21.44/21.53  3672 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset.  [resolve(877,b,824,a)].
% 21.44/21.53  3673 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B.  [resolve(877,b,825,a)].
% 21.44/21.53  3674 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset.  [resolve(877,b,826,a)].
% 21.44/21.53  3675 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B.  [resolve(877,b,827,a)].
% 21.44/21.53  3676 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B.  [resolve(877,b,828,a)].
% 21.44/21.53  3677 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A).  [resolve(877,b,829,b)].
% 21.44/21.53  3678 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A).  [resolve(877,b,830,b)].
% 21.44/21.53  3679 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A).  [resolve(877,b,831,a)].
% 21.44/21.53  3680 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A).  [resolve(877,b,832,a)].
% 21.44/21.53  3681 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A).  [resolve(877,b,833,a)].
% 21.44/21.53  3682 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A).  [resolve(877,b,834,a)].
% 21.44/21.53  3683 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A).  [resolve(877,b,835,a)].
% 21.44/21.53  3684 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A).  [resolve(877,b,836,a)].
% 21.44/21.53  3685 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A).  [resolve(877,b,837,a)].
% 21.44/21.53  3686 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A).  [resolve(877,b,838,a)].
% 21.44/21.53  3687 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A).  [resolve(877,b,839,a)].
% 21.44/21.54  3688 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B.  [resolve(877,b,840,a)].
% 21.44/21.54  3689 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A).  [resolve(877,b,841,a)].
% 21.44/21.54  3690 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A).  [resolve(877,b,842,a)].
% 21.44/21.54  3691 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A).  [resolve(877,b,843,a)].
% 21.44/21.54  3692 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A).  [resolve(877,b,844,a)].
% 21.44/21.54  3693 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B.  [resolve(877,b,845,a)].
% 21.44/21.54  3694 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A).  [resolve(877,b,846,a)].
% 21.44/21.54  3695 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A).  [resolve(877,b,847,a)].
% 21.44/21.54  3696 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A).  [resolve(877,b,848,a)].
% 21.44/21.54  3697 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A).  [resolve(877,b,849,a)].
% 21.44/21.54  3698 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A).  [resolve(877,b,850,a)].
% 21.44/21.54  3699 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C.  [resolve(877,b,851,a)].
% 21.44/21.54  3700 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C.  [resolve(877,b,852,a)].
% 21.44/21.54  3701 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C.  [resolve(877,b,853,a)].
% 21.44/21.54  3702 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(877,b,854,a)].
% 21.44/21.54  3703 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)).  [resolve(877,b,855,a)].
% 21.44/21.54  3704 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A).  [resolve(877,b,856,a)].
% 21.44/21.54  3705 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A).  [resolve(877,b,857,a)].
% 21.44/21.54  3706 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A).  [resolve(877,b,858,a)].
% 21.44/21.54  3707 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)).  [resolve(877,b,859,a)].
% 21.44/21.54  3708 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)).  [resolve(877,b,860,a)].
% 21.44/21.54  3709 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C.  [resolve(877,b,861,a)].
% 21.44/21.54  3710 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(877,b,862,a)].
% 21.44/21.54  3711 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)).  [resolve(877,b,863,a)].
% 21.44/21.54  3712 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B.  [resolve(1063,b,1046,a)].
% 21.58/21.65  3713 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B.  [resolve(1086,b,1069,a)].
% 21.58/21.65  3714 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A).  [resolve(1574,b,1542,a)].
% 21.58/21.65  3715 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1543,a)].
% 21.58/21.65  3716 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1544,a)].
% 21.58/21.65  3717 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset.  [resolve(1574,b,1545,a)].
% 21.58/21.65  3718 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A).  [resolve(1574,b,1546,a)].
% 21.58/21.65  3719 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)).  [resolve(1574,b,1547,a)].
% 21.58/21.65  3720 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A).  [resolve(1574,b,1548,a)].
% 21.58/21.65  3721 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)).  [resolve(1574,b,1549,a)].
% 21.58/21.65  3722 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset.  [resolve(1574,b,1550,a)].
% 21.58/21.65  3723 -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A).  [resolve(1574,b,1551,a)].
% 21.58/21.65  3724 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A).  [resolve(1574,b,1552,a)].
% 21.58/21.65  3725 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1596,a)].
% 21.58/21.65  3726 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1637,b,1597,a)].
% 21.58/21.65  3727 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A).  [resolve(1637,b,1598,a)].
% 21.58/21.65  3728 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1599,a)].
% 21.58/21.65  3729 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1637,b,1600,a)].
% 21.58/21.65  3730 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A).  [resolve(1637,b,1601,a)].
% 21.58/21.65  3731 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A).  [resolve(1637,b,1602,a)].
% 21.58/21.65  3732 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A).  [resolve(1637,b,1603,a)].
% 21.58/21.65  3733 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A).  [resolve(1637,b,1604,a)].
% 21.58/21.65  3734 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A).  [resolve(1637,b,1605,a)].
% 21.58/21.65  3735 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A).  [resolve(1637,b,1606,a)].
% 21.58/21.65  3736 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A).  [resolve(1637,b,1607,a)].
% 21.58/21.65  3737 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A).  [resolve(1637,b,1608,a)].
% 21.58/21.65  3738 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A).  [resolve(1637,b,1609,a)].
% 21.58/21.65  3739 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A).  [resolve(1637,b,1610,a)].
% 22.83/22.90  3740 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A).  [resolve(1637,b,1611,a)].
% 22.83/22.90  3741 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A).  [resolve(1637,b,1612,a)].
% 22.83/22.90  3742 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A).  [resolve(1637,b,1613,a)].
% 22.83/22.90  3743 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A).  [resolve(1637,b,1614,a)].
% 22.83/22.90  3744 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A).  [resolve(1637,b,1615,a)].
% 22.83/22.90  
% 22.83/22.90  ============================== end predicate elimination =============
% 22.83/22.90  
% 22.83/22.90  Auto_denials:  (non-Horn, no changes).
% 22.83/22.90  
% 22.83/22.90  Term ordering decisions:
% 22.83/22.90  Function symbol KB weights:  tc_IntDef_Oint=1. tc_nat=1. c_0=1. c_emptyset=1. c_1=1. c_Finite__Set_OFinites=1. c_List_Olist_ONil=1. c_IntDef_ONats=1. c_Numeral_OPls=1. c_Numeral_Obit_OB1=1. c_Numeral_Obit_OB0=1. c_UNIV=1. c_Numeral_OMin=1. tc_List_Onibble=1. c_Relation_OId=1. c_IntDef_OInts=1. c_IntDef_Ointrel=1. c_Datatype_Ooption_ONone=1. t_c=1. c_IntDef_OInteg=1. c_Wellfounded__Relations_Oless__than=1. c_Extraction_Osumbool_OLeft=1. c_Extraction_Osumbool_ORight=1. c_List_Onibble_ONibble0=1. c_List_Onibble_ONibble1=1. c_List_Onibble_ONibble2=1. c_List_Onibble_ONibble3=1. c_List_Onibble_ONibble4=1. c_List_Onibble_ONibble5=1. c_List_Onibble_ONibble6=1. c_List_Onibble_ONibble7=1. c_List_Onibble_ONibble8=1. c_List_Onibble_ONibble9=1. c_List_Onibble_ONibbleA=1. c_List_Onibble_ONibbleB=1. c_List_Onibble_ONibbleC=1. c_List_Onibble_ONibbleD=1. c_List_Onibble_ONibbleE=1. c_List_Onibble_ONibbleF=1. c_Product__Type_OUnity=1. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. tc_Product__Type_Ounit=1. t_b=1. tc_List_Ochar=1. tc_bool=1. v_x=1. v_xa=1. v_xb=1. c_Numeral_Onumber__of=1. c_uminus=1. tc_fun=1. c_NatArith_Oof__nat=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. c_SetInterval_OlessThan=1. tc_prod=1. c_Finite__Set_OMax=1. c_Finite__Set_OMin=1. c_SetInterval_OgreaterThan=1. c_Numeral_OBit=1. tc_Datatype__Universe_Onode=1. c_HOL_Oabs=1. c_Nat_Osize=1. c_Numeral_Obin__add=1. c_List_Oset=1. c_HOL_Oinverse=1. c_IntDef_Oof__int=1. c_List_Orev=1. c_OrderedGroup_Onprt=1. c_OrderedGroup_Opprt=1. c_Union=1. c_List_Olists=1. c_Transitive__Closure_Ortrancl=1. c_Finite__Set_Ocard=1. c_Inter=1. c_List_Oremdups=1. c_List_Oupt=1. c_List_Olast=1. c_List_Oconcat=1. c_List_Olistrel=1. c_List_Olex=1. c_Pow=1. c_Datatype_Ooption_OSome=1. c_Numeral_Obin__mult=1. c_Relation_Odiag=1. tc_sum=1. c_Binomial_Obinomial=1. c_List_Olexord=1. c_List_Orotate1=1. c_List_Obutlast=1. c_List_Ohd=1. c_List_Otl=1. c_Transitive__Closure_Otrancl=1. c_Datatype_Oo2s=1. c_List_Ochar_OChar=1. c_IntDiv_Oadjust=1. c_List_Olistset=1. c_Main_OIdE__1=1. c_Main_OInter__UNIV__conv__1__1=1. c_Main_OInter__UNIV__conv__2__1=1. c_Main_ONil__eq__concat__conv__1=1. c_Main_OUnion__empty__conv__1=1. c_Main_Oconcat__eq__Nil__conv__1=1. c_Main_Oempty__Union__conv__1=1. c_Main_Ofinite__Union__1=1. v_h=1. c_Datatype_Othe=1. c_Fun_Oid=1. c_List_Olenlex=1. c_Main_Oall__not__in__conv__1=1. c_Main_Olexord__Nil__left__1=1. c_Main_Olexord__Nil__left__2=1. c_Main_Omod__eq__0D__dest__1=1. c_Main_Onot__None__eq__1=1. c_Main_Onot__Some__eq__1=1. c_Main_Ozmod__eq__0D__dest__1=1. c_Set_Ocontents=1. v_f=1. tc_set=1. tc_List_Olist=1. c_Suc=1. c_Numeral_Obin__minus=1. c_IntDef_Oint=1. c_IntDef_Onat=1. c_GCD_Ogcd=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Numeral_Obin__pred=1. c_IntDiv_OnegateSnd=1. c_Numeral_Obin__succ=1. c_IntDef_OAbs__Integ=1. tc_Datatype_Ooption=1. c_IntDef_ORep__Integ=1. v_A=1. c_times=1. c_plus=1. c_SetInterval_OatLeastLessThan=1. c_minus=1. c_insert=1. c_divide=1. c_Orderings_Omin=1. c_Orderings_Omax=1. c_Nat_Opower=1. c_SetInterval_OatLeastAtMost=1. c_List_Olist_OCons=1. c_SetInterval_OgreaterThanAtMost=1. c_Divides_Oop_Amod=1. c_append=1. c_SetInterval_OgreaterThanLessThan=1. c_div=1. c_inter=1. c_union=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=1. c_Main_OMax__le__iff__1=1. c_Main_OMax__less__iff__1=1. c_Main_OMin__ge__iff__1=1. c_Main_OMin__gr__iff__1=1. c_List_Onth=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_Datatype__Universe_OIn0=1. c_Datatype__Universe_OIn1=1. c_Relation_ODomain=1. c_Relation_Oconverse=1. c_List_Orotate=1. c_Relation_ORange=1. c_fst=1. c_snd=1. c_List_Oremove1=1. c_List_Osublist=1. c_SetsAndFunctions_Oelt__set__plus=1. c_SetsAndFunctions_Oelt__set__times=1. c_Sum__Type_OInl=1. c_Sum__Type_OInr=1. c_List_Olist__inter=1. c_Datatype__Universe_OAtom=1. c_Datatype__Universe_OLeaf=1. c_Datatype__Universe_ONumb=1. c_Equiv__Relations_Oquotient=1. c_List_Oitrev=1. c_Main_OdiagE__1=1. c_Main_OInterI__1=1. c_Main_OInter__iff__1=1. c_Main_OUnionE__1=1. c_Main_OUnion__iff__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Datatype_Ounit_Ounit__case=1. c_Datatype_Ounit_Ounit__rec=1. c_List_Olexn=1. c_List_Oset__Cons=1. c_Main_Osurj__pair__1=1. c_Main_Osurj__pair__2=1. c_Pair=1. c_Relation_OImage=1. c_Datatype__Universe_Ontrunc=1. c_Datatype__Universe_OScons=1. c_List_Ozip=1. c_List_Olist__update=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Datatype__Universe_Odprod=1. c_Datatype__Universe_Ouprod=1. c_Main_OPlusE__1=1. c_Main_OPlusE__2=1. c_Main_OdsumE__1=1. c_Main_OdsumE__2=1. c_Main_OdsumE__3=1. c_Main_OdsumE__4=1. c_Main_OusumE__1=1. c_Main_OusumE__2=1. c_Extraction_Osumbool_Osumbool__case=1. c_Extraction_Osumbool_Osumbool__rec=1. c_Main_OconverseE__1=1. c_Main_OconverseE__2=1. c_Numeral_Obit_Obit__case=1. c_Numeral_Obit_Obit__rec=1. c_Wellfounded__Relations_Olex__prod=1. c_Main_ODomainE__1=1. c_Main_ORangeE__1=1. c_Map_Omap__of=1. c_Relation_Orel__comp=1. c_Main_OImageE__1=1. c_Main_OdprodE__1=1. c_Main_OdprodE__2=1. c_Main_OdprodE__3=1. c_Main_OdprodE__4=1. c_Main_Olistrel__Cons1__1=1. c_Main_Olistrel__Cons1__2=1. c_Main_Olistrel__Cons2__1=1. c_Main_Olistrel__Cons2__2=1. c_Main_OuprodE__1=1. c_Main_OuprodE__2=1. c_Main_Orel__compE__1=1. c_Main_Orel__compE__2=1. c_Main_Orel__compE__3=1. c_List_Onibble_Onibble__case=1. c_List_Onibble_Onibble__rec=1.
% 22.83/22.90  
% 22.83/22.90  ============================== PROOF =================================
% 22.83/22.90  % SZS status Unsatisfiable
% 22.83/22.90  % SZS output start Refutation
% 22.83/22.90  
% 22.83/22.90  % Proof 1 at 21.45 (+ 0.02) seconds.
% 22.83/22.90  % Length of proof is 3.
% 22.83/22.90  % Level of proof is 1.
% 22.83/22.90  % Maximum clause weight is 6.000.
% 22.83/22.90  % Given clauses 0.
% 22.83/22.90  
% 22.83/22.90  5601 c_lessequals(c_0,v_h(A,B),t_c) # label(cls_conjecture_0) # label(negated_conjecture).  [assumption].
% 22.83/22.90  5604 -c_lessequals(c_0,v_h(v_xa,v_xb),t_c) # label(cls_conjecture_3) # label(negated_conjecture).  [assumption].
% 22.83/22.90  5605 $F.  [copy(5604),unit_del(a,5601)].
% 22.83/22.90  
% 22.83/22.90  % SZS output end Refutation
% 22.83/22.90  ============================== end of proof ==========================
% 22.83/22.90  
% 22.83/22.90  ============================== STATISTICS ============================
% 22.83/22.90  
% 22.83/22.90  Given=0. Generated=1563. Kept=1477. proofs=1.
% 22.83/22.90  Usable=0. Sos=0. Demods=382. Limbo=1477, Disabled=5466. Hints=0.
% 22.83/22.90  Megabytes=17.84.
% 22.83/22.90  User_CPU=21.45, System_CPU=0.02, Wall_clock=22.
% 22.83/22.90  
% 22.83/22.90  ============================== end of statistics =====================
% 22.83/22.90  
% 22.83/22.90  ============================== end of search =========================
% 22.83/22.90  
% 22.83/22.90  THEOREM PROVED
% 22.83/22.90  % SZS status Unsatisfiable
% 22.83/22.90  
% 22.83/22.90  Exiting with 1 proof.
% 22.83/22.90  
% 22.83/22.90  Process 5016 exit (max_proofs) Fri Jul  8 05:58:47 2022
% 22.83/22.90  Prover9 interrupted
%------------------------------------------------------------------------------